Problem 97 - Algebra A Combined Function

Question

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

Step-by-Step Solution

Answer

a. 52.9% b. 52.86%

Step 1: Understanding the Problem

We are given a percentage, which is 52.8647%, and we need to round it first to the nearest tenth percent and then to the nearest hundredth percent.

Step 2: Rounding to the Nearest Tenth Percent

To round to the nearest tenth, we look at the first decimal place (tenths place), which is 8. We then check the second decimal place to the right (hundredths place), which is 6. Since 6 is greater than 5, we round up the tenths place from 8 to 9. So, 52.8647% becomes 52.9% when rounded to the nearest tenth percent.

Step 3: Rounding to the Nearest Hundredth Percent

To round to the nearest hundredth, we look at the second decimal place (hundredths place), which is 6. We then check the third decimal place to the right (thousandths place), which is 4. Since 4 is less than 5, we do not change the hundredths place, so 52.8647% remains 52.86% when rounded to the nearest hundredth percent.

Key Concepts

Tenth percent rounding

Rounding to the nearest tenth percent helps simplify a percentage by focusing on the first decimal place after the whole number. Think of tenth percent rounding as zooming in on the first digit after the decimal. This is the tenths place, an important spot because it can shift the whole number if needed. To effectively round a percentage like 52.8647% to the nearest tenth percent, follow these easy steps:

• Identify the tenths place. For 52.8647%, this is the 8 right after the decimal point.
• Check the digit right after the tenths place, which here is the 6 (hundredths place).
• If this digit is 5 or more, we round up the tenths place value. So, since 6 is more than 5, we increase the 8 to 9.
• Result: 52.8647% becomes 52.9% after rounding to the nearest tenth percent.

Rounding like this helps make large or complex percentages easier to work with, especially in reports or calculations where precision is still needed but in a simpler form.

Hundredth percent rounding

To gain slightly more accuracy in your results, you might round to the nearest hundredth percent. This involves a closer examination of the number by looking at more digits after the decimal point. Specifically, hundredth percent rounding examines the second and third decimal places in your number. For example, to round 52.8647% to the nearest hundredth percent:

• Focus on the second decimal digit, which is 6 in this example.
• The digit after the 6 is 4, located in the thousandths place.
• If this following digit is 5 or higher, increase the hundredths digit by one. But since 4 is less than 5, we leave the value of 6 unchanged.
• Therefore, 52.8647% is rounded to 52.86%.

Hundredth percent rounding is particularly useful when precision is key and small differences can have an impact, like in financial calculations.

Decimal place value

Understanding decimal place value is essential in rounding percentages, as it determines how you perceive the importance of each digit in the decimal expansion. Decimal place value orders the digits in a number by their position, with each position having a unique quantitative significance. Here's how decimal place value works:

• The first place after the decimal point is called the "tenths place," affecting the first rounding decision.
• The next is the "hundredths place," giving another level of detail when doubling the precision in rounding.
• Following that, the "thousandths place" helps decide how the hundredths place is handled in rounding.

For percentages like 52.8647%, knowing the placement of digits (5, 2, 8, 6, 4, 7) ensures you make the right choice when rounding based on the significance of each decimal's place value. This understanding helps maintain the accuracy of numbers while simplifying them for practical use.