Question

Copy and complete the table. If necessary, round to the nearest tenth of a percent. $$\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \text { Decimal } & ? & 0.2 & ? & 0.073 & 0.666 \ldots & ? & ? & 2 \\\\\hline \text { Percent } & 78 \% & ? & 3 \% & ? & ? & 176 \% & 110 \% & ? \\\\\hline\end{array}$$

Short answer

The completed table is: Decimal values: ?, 0.2, ?, 0.073, 0.666 ... , ?, ?, 2; Percentages: 78%, 20%, 3%, 7.3%, 66.6%, 176%, 110%, 200%.

Step-by-step solution

Fill in first missing decimal

Given that 78% is equal to 0.78 in decimal. Divide a percent by 100 to turn it into a decimal. Thus the first missing decimal will be 0.78.

Turn second decimal to percentage

Multiplying the decimal 0.2 by 100, gives us 20, so 0.2 as a percentage is 20%. Thus the second missing percentage will be 20%.

Fill in third missing decimal

Given that 3% is equal to 0.03 in decimal. Divide a percent by 100 to turn it into a decimal. So, the third missing decimal will be 0.03.

Turn Fourth decimal to percentage

Multiplying the decimal 0.073 by 100, gives us 7.3, so 0.073 as a percentage is 7.3%. Thus the fourth missing percentage will be 7.3%.

Turn Fifth decimal to percentage

Multiplying the decimal 0.666 repeating by 100, gives us 66.6 repeating, so 0.666 repeating as a percentage is 66.6(repeating)%. Thus the fifth missing percentage will be 66.6%.

Fill in sixth missing decimal

Given that 176% is equal to 1.76 in decimal. Divide a percent by 100 to turn it into a decimal. Thus the sixth missing decimal will be 1.76.

Fill in seventh missing decimal

Given that 110% is equal to 1.10 in decimal. Divide a percent by 100 to turn it into a decimal. Thus the seventh missing decimal will be 1.10.

Turn eight decimal to percentage

Multiplying the decimal 2 by 100, gives us 200, so 2 as a percentage is 200%. Thus the eight missing percentage will be 200%.

Key concepts

Decimal to Percent Conversion

Understanding decimal to percent conversion is essential for interpreting data that comes in various forms. The process is surprisingly straightforward. To convert a decimal to a percent, you simply multiply the decimal number by 100 and add a percent sign (%).

For example, to convert 0.2 to a percent, you multiply 0.2 by 100, which gives you 20, and then you add the percent sign to get 20%. It's a simple multiplication that transforms the decimal into a much more familiar percentage for many of us.

Real-World Application

Decimal to percent conversion is not just a math exercise; it's used in financial reporting, statistics, and even when comparing discounts during shopping. For accommodating such tasks, often a calculator or cell functions in spreadsheets can be used to ease the process.

Percent to Decimal Conversion

On the flip side, converting percentages to decimals is a common necessity as well. This is just as simple but goes in the opposite direction. To convert a percent to a decimal, divide the percent value by 100 and remove the percent sign.

For instance, to convert 78% to a decimal, divide 78 by 100 to get 0.78. This is useful in many practical calculations, like determining the decimal form for interest rates or statistical data.

Tip for Remembering

A practical tip for remembering this conversion is to think about the percent sign (%) as a reminder to either move the decimal point two places to the right when converting to a percent or two places to the left when converting to a decimal.

Rounding Decimals

When converting between decimals and percents, you may sometimes encounter numbers with many decimal places. In such cases, rounding helps to simplify the number. Rounding rules tell us to look at the digit to the right of our rounding position; if it's 5 or higher, we round up, and if it's 4 or lower, we round down.

For instance, if we're rounding 0.666 repeating to the nearest tenth, we look at the first two digits after the decimal. Since the second digit is a 6, we round up the first digit to a 7, and our rounded number becomes 0.7 or 70% when converted to a percent.

Consistency in Rounding

Consistency is critical when rounding, especially in financial contexts or academic settings. Always apply the same rounding rules to ensure transparency and to prevent cumulative errors in calculations or reporting.