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Chapter 7: Problem 93

Given the percent \(52.8647 \%,\) round as indicated. a. Round to the nearest tenth percent. b. Round to the nearest hundredth percent.

Short Answer

Expert verified
a. 52.9% b. 52.86%

Step by step solution

01

Understanding the Problem

We have been given a percentage value: 52.8647%. Our task is to round this percentage to different places: nearest tenth and nearest hundredth.
02

Round to the Nearest Tenth Percent

To round 52.8647% to the nearest tenth, we need to look at the digit in the hundredths place, which is 6. Since 6 is greater than 5, we round up, resulting in 52.9%.
03

Round to the Nearest Hundredth Percent

To round 52.8647% to the nearest hundredth, we look at the digit in the thousandths place, which is 4. Since 4 is less than 5, we do not round up. Thus, the result is 52.86%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nearest Tenth
Rounding a number to the nearest tenth means we aim for one digit after the decimal point. In the percentage 52.8647%, the digit in the tenths place is 8. To decide whether 52.8 should stay or become 52.9, look at the digit immediately to the right, which is the 6 in the hundredths place.
According to rounding rules, if this digit is 5 or more, we round up. Since 6 is greater than 5, we round 52.8 up to 52.9. Thus, 52.8647% rounded to the nearest tenth becomes 52.9%.
  • Tenths place in percentage: Represents the first decimal place.
  • Check digit in next place for rounding: Hundredths place here.
  • If 5 or more, round up the tenths digit.
Nearest Hundredth
When rounding to the nearest hundredth, you focus on ensuring two digits after the decimal. For 52.8647%, you look at these digits: 86.
The digit in the thousandths place, right after the hundredths, helps decide rounding. With our number, the digit is 4. If it's 5 or more, you increase the hundredths place by one. Here, since 4 is less than 5, 86 stays the same. Thus, 52.8647% rounded to the nearest hundredth is 52.86%.
  • Hundredths place: Two digits after the decimal.
  • Consider thousandths place to determine rounding.
  • Less than 5, keep it; 5 or more, round up.
Place Value
Understanding place value is key when rounding percentages. It's about identifying the "worth" of a digit based on its position. Each position in a decimal number has a specific value:
  • The first digit to the right of the decimal is the tenths place, which is 0.1 times the main number.
  • The next digit is the hundredths place, worth 0.01 times the number.
  • The third is the thousandths, or 0.001 times the number.
For the number 52.8647%, the digits 8, 6, 4, and 7 fall into these places: 8 is in the tenths, 6 in the hundredths, 4 in the thousandths, and 7 in the ten-thousandths place. Each determines rounding choices based on their established place value.
Rounding Rules
Rounding rules provide a path to simplify numbers while maintaining accuracy. These rules help decide whether to increase the last retained digit based on the next digit over. Here鈥檚 how it works:
  • If the next digit is 5 or higher, increase the target digit by one.
  • If it's 4 or lower, keep the target digit as it is.
  • These rules ensure consistency across different mathematical and real-world scenarios.
In the case of 52.8647%, rounding rules dictate that for the nearest tenth, the 6 results in rounding up the 8 to a 9. For the nearest hundredth, the 4 means the 6 stays the same. Following these guidelines is crucial in acquiring rounded numbers that reflect true rounded values.

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Most popular questions from this chapter

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