Placement chart for decimals: Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

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Learn Definition, Facts and Examples

The place values of the digits in a decimal number are displayed on the decimal place value chart. We know that a digit in a number represents a numerical value or place value.

Decimal place value charts are used to determine the proper placement of each digit in a decimal number. The place values of the digits given before and after the decimal point are displayed.

Place Value in Decimal

Place Value Definition in Decimals

A decimal number consists of a whole number and a fractional component, separated by the decimal point, a dot.

For instance, the decimal number 4.37 has two parts: an actual number portion of 4 and a fractional portion of 37. The place values of all digits are displayed in a decimal place value chart.

This is How we Deduct Values after Decimal Points.

The place values often represented by the digits preceding the decimal point are ones, tens, hundreds, thousands, and so forth. While the place values represented by the numbers after the decimal point begin with the tenth, moving up through the hundredths and thousandth.

Place Value Chart

Chart of Decimal Place Values

Representation of Decimal Values

The place values before the decimal point start with ones, followed by tens, and so forth, while the place values following the decimal point start from tenths, followed by hundredths, then thousandths, and so forth. The fractional portion of the number is represented by the place value that follows the decimal. The number 0.56, for instance, is composed of 5 tenths and 6 hundredths. This can be expressed as 0.56 = 0.5 + 0.06. In other terms, 0.56 is $\dfrac{5}{10} \text { plus } \dfrac{6}{100}$.

Solved Examples

1. Write the place value of the digits 2 and 4 in the number 326.471

Ans: The steps to solve this problem is as follows:

• First, write the number in a decimal place value chart.

• Then, look at the digit’s place and find its place value.

• The digit 2 is in the tens place. Therefore, its place value is 2 tens or 20.

• The digit 4 is in tenth place. Therefore, its place value is four-tenths of 0.4

2. Find the place value of the underlined digits in the number 4532.079

Ans: The steps to solve this problem is as follows:

• In the number 4532.079:

• 4 is at the thousands place. So, its place value is 4 thousands or 4000

• 0 is in tenth place. So, its place value is 0 tenths or 0

• 9 is at the thousandth place. So, its place value is 9 thousandths of 0.009

Fun Facts About Decimal Place Value

• The actual value of a digit is called its face value. Unlike the place value of an integer, which depends upon its position in a number, the face value remains the same, irrespective of its class.

• Have you ever been told to multiply by ten, and add zero at the end? If so, you’ve been misled! Here’s an example: 2.3 x 10 is not 2.30. It is 23.0. When you multiply by ten, every digit shifts along with one place to the left. So, in our example, there are 2 tens rather than 2.

• The ‘dec’ in decimal means ten and refers to the fact that each position in a decimal number corresponds to ten times more than the next. For example, the number 325.31 means 3 hundred, 2 tens, 5 ones, 3 tenths, and 1 hundredth. Humans decided to group in tens because that’s how many fingers/thumbs we have. It made counting and arithmetic a whole lot easier. Three-fingered aliens might well group in threes!

Practice Questions

Q 1. Write the place value of the digits 6 and 4 in the number 926.894

Ans: 6 = ones and 4 = thousandths

Q 2. Write the place value of the digit 2 in the number 73.42

Ans: Hundredths

Summary

By adding decimal places, we can conclude that the base-10 number system may now express fractional numbers and unlimited amounts. To count parts or fractions of things, we utilize decimals. These are the numbers that appear on the number line in between the whole numbers. The decimal places are endlessly on the left and get smaller and smaller as you move along.

1.6 Using Decimals | NWCG

DECIMAL NUMBERS

How a number is read depends on where the decimal point is placed. The figure below is similar to the chart for large numbers in Section 1.1. The decimal point comes after the ones position. The numbers to the right of the decimals represent tenths (0.1), hundreds (0.01), thousands (0.001), and so on down to infinitesimally small numbers.

All whole numbers (called integers) have a decimal point at the end. For instance, 10 = 10., 24 = 24., and 17,801 = 17,801 = 17,801.0.

MULTIPLES OF 10

Decimals correspond to multiples of 10. Note that the numbers 10, 100, 1000, 10,000 and so on are written similarly except for the number of «0»s between the first digit and the decimal point. This fact allows for division using these numbers to work by simply moving the decimal place. To divide by a factor of 10, count the number of zeros in the divisor or denominator and move the decimal point that many spaces to the left.

Consider 100/10, which can be written 100.0/10.0.

There is one zero in the 10, so move the decimal point in the 100 to the left by one place. 100/10 = 10.

Example 1 — Compute 8679 ÷ 1000. There are three zeros in 1000. Move the decimal point three places to the left, remembering that whole numbers have a decimal point at the end.

We can write 8679 ÷ 1000 = 8679. ÷ 1000. = 8.679

SIGNIFICANT FIGURES AND ROUNDING FOR ACCURACY

A decimal place indicates the accuracy of the given number. The accuracy of an answer is determined by the lowest level of accuracy of the original numbers being added, subtracted, multiplied, or divided. Accuracy does not improve with addition, subtraction, multiplication, or division. This detail is especially important for performing multiplication and division with decimal places.

Example 2 — What is 8.2 + 0.25? The lowest level of accuracy is to the 0.1 (or 1/10th) decimal place, so the correct answer is to the 1/10th decimal place. Rounding up or down is a method of bringing the answer to the correct level of accuracy. 8.2 + 0.25 = 8.45. However, the answer is only accurate to the 1/10th. What is 8.45 to the nearest 1/10th? To get the answer to the appropriate accuracy, round up or round down the digit beyond the lowest level of accuracy. If the number to be rounded is 5, 6, 7, 8, or 9, round up. Round down if the numbers are 4, 3, 2, or 1.

For 8.2 + 0.25 = 8.45, round up the 0.45 to 0.5. The answer of 8.5 has the correct accuracy.

Example 3 — What is 986.525 minus 459.83?

Performing the subtraction yields the result 526.695. The lowest level of accuracy is to the 0.01 (1/100ths) decimal place, so the digit in the 0.001 (1/1000ths) place must be rounded up or down. The last digit is a 5, so we round up and express the answer as 986.525 — 459.83 = 526.70.

When adding, subtracting, multiplying, or dividing digits, all numbers must have the same number of significant digits as the least accurate original number.

Example 4 — A helicopter landing pad is in the shape of the six-sided figure below.
Side A is 12.50 feet long.
Side B is 6.57 feet long.
Side C is 7.8 feet long.
Side D is 11.00 feet long.
Side E is 5.5 feet long.
Side F is 8.15 feet long.
What is the total perimeter of the helicopter pad?

This problem involves adding numbers that are written using decimal notation.
First, set up the sum: 12.50 + 6.57 + 7.8 + 11.00 + 5.5 + 8.15 = 51.52

Now, check to see that your answer is expressed the correct accuracy. The lowest level of accuracy is the 0.1 (1/10ths) decimal place, as expressed by 7.8 and 5.5. Rounding the 0.01 (1/100ths) place digit, we express the perimeter of the helicopter pad as 51.5 feet.

MULTIPLICATION WITH DECIMALS

Accuracy in an answer is indicated by placement of the decimal point when multiplying numbers.

In multiplication, determine the correct decimal point after the multiplication is complete. After the numbers have been multiplied, count the number of places to the right of both of the original numbers. The lower amount of decimal places is then applied to the product as the number of places to the right of the decimal.

Example 5 — Multiply 0.9 × 1.53.

In this example, 1.377 has three decimal places, but the lowest accuracy number involved in the multiplication (0.9) has 0.1 (1/10ths) accuracy. Round the answer to the tenths place: 0.9 × 1.53 = 1.4

DIVISION WITH DECIMALS

When performing division, it is important to look at the dividend, which is the number that is being divided. Long division is performed by placing the decimal point in the answer directly above the decimal point in the number being divided.

Example 6 — Compute 89.76 ÷ 12

In this case, the answer 7.48 has the same number of decimal places as the dividend.

If the divisor is not a whole number, the decimal places need to be moved in both the divisor and dividend to make sure that the decimal in the quotient is correctly placed. First, move the decimal point in the divisor to the right to make the number into a whole number, or integer. Then, move the decimal point in the number being divided (the dividend) to the right by the same number of spaces. Now, place the decimal point directly above the point in the number being divided and divide as though dividing whole numbers.

Example 7 — Divide 4.067 / 0.83.
To make the divisor a whole number, the decimal point must be moved two places to the right so the divisor becomes 83. The decimal point must also be moved in the dividend, so that the dividend becomes 406.7

Now, long division proceeds as with whole numbers, and the answer to 406.7/0.83 is 4.9.

One tip for working with decimals is to ask yourself, «does that answer make sense»? If you are adding or multiplying whole numbers (integers), your end result should be larger then the numbers being multiplied. If you are subtracting or dividing whole numbers (integers), your result should be smaller. We can do a quick check of the division involving decimals in Example 7 by the looking the numbers being divided. In this case, we are dividing a number slightly larger than 4, by a number slightly smaller than 1. We can compute that 4 ÷ 1 is 4, so our number should be somewhat close to that. It should not be 40, or 0.4, or 400. In doing calculations in the field, look carefully at the numbers involved, and the operation (addition, multiplication, etc.). In many situations, the answer can be imperative to your safety, so make sure that the end result makes sense.

Create and use a combo chart—ArcGIS Insights

A combo chart is a combination of two bar charts, two line charts, or a bar chart with a line chart. You can create a combo chart with one dataset or two datasets that share a common string field.

Combination charts can answer questions about data such as: What are the trends for the same categories?

Example

An environmental organization is tracking the location of the Southern California drylands and wants to compare temperatures and rainfall to determine which cities are most vulnerable to drought. This organization will use a combo chart to display total rainfall and average temperature for each city in one chart.

Creating a combo chart

You can create a combo chart with one dataset or with two datasets that have a common string field.

One dataset

To create a combo chart with one dataset, complete the following steps:

1. Select a string field and two numeric or rate/ratio fields.
2. Follow these steps to create a combo chart:
1. Drag the selected fields to a new card.
2. Move the cursor over the Chart placement area.
3. Drag the selected fields to the Combo Chart.
Hint:

You can also build charts using the Chart menu above the data panel or the Visualization Type button on an existing card. In the Charts menu, only charts that are applicable to the existing data selection will be available. The Visualization Type menu will display only suitable visualization options (maps, charts, or tables).

Two datasets with a common string field

To create a combo chart on top of an existing column or line chart, do the following:

1. Select one of the following data options:
• Numeric or rate/ratio field from the same dataset as the existing chart.
• A string field corresponding to the existing chart’s string field, plus a numeric or rate/ratio field from a different dataset than the one used in the existing chart.
2. Drag the selected fields onto an existing bar or line chart.
3. Drag the fields to the Combo Chart drop area.
4. Optionally change the chart type using the Graph Chart or Column Chart buttons located on the vertical axes.

Usage Notes

The Layer Options button opens the Layer Options panel. You can use the Layer Options panel to view the legend, change chart options, and update the chart style.

The Legend tab displays symbols for the bar chart and graph. The popup legend button will display the legend as a separate card on your page. When unique symbols are used, a Legend can be used to select data in a bar chart. To change the color associated with a category, click the icon and select a color from the palette, or enter a hexadecimal value.

The Symbology tab is used to change the Symbol Type to Unique symbol for bars, line smoothing for a line plot, y-axis synchronization, and labeling on or off.

The Synchronize y-axes check box can be used to bring both axes to the same scale. Using the same scale for both y-axes is useful when your variables use a similar scale, or you want to analyze the magnitude of the difference between variables.

Labels display the numeric values ​​associated with the chart. The following settings are available for labels:

• Decimals — you can select the number of decimal places for labels from zero to five, or select Default or Auto. The default will truncate large numbers, and Auto will choose an appropriate precision.
• Label Alignment — Three alignment options are available for combo charts: Horizontal, Outside, Vertical, Outside, and Angled.
• Contextual label — symbols can be added to the label, such as an icon or a unit of measure. The context label can be placed to the left (default) or to the right of the value.

The Appearance tab is used to change the symbol color for both the bar chart (single symbol only) and line chart, change the bar chart outline color, change the chart template and thickness.

The value of each bar and trend line can be indicated as the number of objects in each category along the x-axis, as a number, or as a percentage/ratio field. If a field is used, then the values ​​can be calculated as the sum, minimum, maximum, mean, percentile, or median of the field values ​​for each of the categories.

Median and percentile are not available for some remote vector layers. If the deleted feature layer does not support median or percentile, you can copy the layer to a workbook.

The Column Chart and Y-Axis Plot Chart buttons can be used to switch between the Column Chart and Line Chart visualization types. If both axes are set to bar chart, then the bars will be sorted into subgroups for each category.

Use the Flip Card button to view the back of the card. The Card Information tab provides information about the data on the card, the Image Export tab allows users to export an image of the card, and the Data Export tab allows users to export card data.

Data export is not available for combo charts created using two datasets.

When you create a combo chart, the result datasets will be added to the data pane with the string and number fields used to create the charts. The resulting dataset can be used when searching for answers in non-spatial analysis using the Action button.

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Create and use a graph chart—ArcGIS Insights

Graph charts display information as a series of data points connected by straight lines. Categories are displayed on the x-axis and statistics on the y-axis. Unlike time series charts, where only date and time can be plotted along the category axis, line charts allow you to use string fields for values ​​on the category axis.

Graph charts can answer questions about your data, such as How are numbers distributed or summarized across categories?

Example

An environmental organization is tracking the location of the southern California drylands and wants to compare rainfall rates across regions to determine which cities are most vulnerable to drought. The organization uses a graph to display the total rainfall for each city.

The graph above shows how rainfall varies by city.

Create new graph 9Ol000 using the following steps:

1. Drag the selected fields to the new card.
2. Move the cursor over the Chart placement area.
3. Place the selected fields on the Graph Chart.
Hint:

Drag the appropriate string field from the second dataset onto the line chart to create a combo chart.

Hint:

You can also build charts using the Chart menu above the data panel or the Visualization Type button on an existing card. In the Charts menu, only charts that are applicable to the existing data selection will be available. The Visualization Type menu will display only suitable visualization options (maps, charts, or tables).

Usage Notes

The Layer Options button opens the Layer Options panel. You can use the Layer Options panel to view the legend, change chart options, and update the chart style.

The Legend tab is used to view the symbols in the chart. The popup legend button will display the legend as a separate card on your page. You can use a legend to create a selection on a chart.

To change the color or hatching associated with a value, click the symbol and select the desired color from the palette, or enter its six-digit code, or select the hatching. Changing the symbol on the Legend tab is only available for unique symbols.

The Symbology tab is used to apply the Smooth line option and turn labels on or off. A smooth line is best when you are showing trends in the data without sudden changes, rather than specific values. For example, displaying trends in monthly temperatures with a smoothed line is well suited for seasonal analysis.

Labels display the numeric values ​​associated with the chart. The following settings are available for labels:

• Decimals — you can select the number of decimal places for labels from zero to five, or select Default or Auto. The default will truncate large numbers, and Auto will choose an appropriate precision.
• Label Alignment — Three alignment options are available for graph charts: Horizontal, Outside, Vertical, Outside, and Angled.
• Contextual Label — Symbols can be added to the label, such as an icon or a unit of measure. The context label can be placed to the left (default) or to the right of the value.

The Appearance tab is used to change the color of a symbol (for a single symbol only) and to change the hatch pattern and line weight.

Changes in a graph can be indicated as a number of objects over time, or as a number field or a rate/ratio field. If a field is used, then the chart values ​​can be calculated as the sum, minimum, maximum, average, percentage, or median of the field values ​​for each point at each point in time.

Median and percentile are not available for some remote vector layers. If the deleted feature layer does not support median or percentile, you can copy the layer to a workbook.

Use the Chart Statistics button to display the mean, median, upper quartile, lower quartile, or custom value.

The Sort button is used to sort categorical data by a numeric variable in either ascending or descending order or alphabetically.

Use the Visualization Type button to switch from a Graph Chart to other visualization types such as a PivotTable, Column Chart, or Bubble Chart.

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