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Chapter 5: Problem 4

For Exercises \(3-5,\) round to the indicated place value. \(-0.399 ;\) hundredths

Short Answer

Expert verified
-0.40

Step by step solution

01

Identify the indicated place value

Locate the hundredths place in the number. The decimal number is -0.399. The digit in the hundredths place is the second digit to the right of the decimal point, which is 9.
02

Identify the digit immediately to the right of the hundredths place

Look at the digit immediately to the right of the hundredths place. In this case, it's the third digit to the right of the decimal point, which is 9.
03

Apply rounding rules

Since the digit immediately to the right of the hundredths place (9) is 5 or greater, round up the digit in the hundredths place (9) by 1. So, 9 becomes 10. But since we can't have two digits in one place value, we set the hundredths place to 0 and add 1 to the tenths place, changing it from 9 to 10. This results in -0.40.

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Key Concepts

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

Place Value
Understanding place value is essential in rounding decimals. Place value refers to the position of each digit in a number, which determines its value. For example, in the number -0.399:
  • - The digit 3 is in the tenths place (first digit to the right of the decimal point).
  • - The digit 9 is in the hundredths place (second digit to the right of the decimal point).
  • - Another digit 9 is in the thousandths place (third digit to the right of the decimal point).
Recognizing each digit's place value helps us apply rounding rules accurately. By identifying the hundredths place and the digit next to it, we can make the correct rounding decisions.
Rounding Rules
Rounding rules are straightforward but crucial when working with decimals. Here is a simple way to remember how to round decimals:
  • Locate the place value you need to round to.
  • Look at the digit immediately to the right of that place value (this is called the critical digit).
  • If the critical digit is 5 or greater, round up the digit in the place value by 1.
  • If the critical digit is less than 5, keep the digit in the place value the same.
Using our example, -0.399 rounded to the hundredths place involves:
- Identifying the hundredths place (second digit to the right of the decimal point, which is 9).
- Looking at the next digit, the thousandths place, which is also 9.
- Since 9 is greater than 5, we round up the digit in the hundredths place from 9 to 10, which pushes the tenths place up, resulting in -0.40.
Decimal Point
The decimal point is a critical marker in a number that separates the whole number part from the fractional part. In the decimal number -0.399:
  • - The decimal point appears just after the negative sign and before the digits 399.
  • - Each digit to the right of the decimal point represents a fractional part of a whole number (tenths, hundredths, thousandths, etc.).
When rounding decimals, the position of the decimal point remains constant. It is the digits around it that change based on rounding rules. For instance, even after rounding -0.399 to -0.40, the decimal point stays in its place, ensuring the number remains properly formatted. Understanding the role of the decimal point aids in accurately interpreting and rounding numbers.

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