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Chapter 5: Problem 12

In the following exercises, name each decimal. $$-31.4$$

Short Answer

Expert verified
Minus thirty-one and four tenths

Step by step solution

01

Identify the Decimal Number

The given number is -31.4.
02

Understand the Place Values

In the number -31.4, the digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts. Specifically, the digit 3 is in the tens place, 1 is in the units place, and 4 is in the tenths place.
03

Construct the Number's Name

Combine the integer part and the fractional part names. The integer part is thirty-one and the fractional part two decimal places away becomes four tenths.
04

Format the Final Answer

By including the sign and combining all elements, thus the final name is: minus thirty-one and four tenths.

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Key Concepts

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

Understanding Place Value
Place value is a crucial concept in mathematics. It helps us determine the value of a digit in a number based on its position. Each position in a number has a specific place value.
For instance, in the number -31.4, each digit has its place value:
  • The digit 3 is in the tens place, meaning it represents three tens or 30.
  • The digit 1 is in the units place (also called the ones place), meaning it represents one unit or 1.
  • The digit 4 is to the right of the decimal point and is in the tenths place, representing four tenths or 0.4.
This system of place value extends infinitely to the left and right, allowing us to represent extremely large and very small numbers efficiently.
Integer Part of a Decimal
The integer part of a decimal number is the part that is to the left of the decimal point. It consists of whole numbers. In the number -31.4, the integer part is -31.
When naming the integer part, we use regular naming conventions like we would with whole numbers. For example:
  • In the number 123.45, the integer part is 123, which is one hundred twenty-three.
  • In -31.4, the integer part is -31, which is minus thirty-one.
The sign of the integer part (positive or negative) is important and must be noted when naming the number.
Fractional Part of a Decimal
The fractional part of a decimal number is the part that comes after the decimal point. It represents fractions of a whole number. In -31.4, the fractional part is 0.4.
To name the fractional part, we refer to the place value of the last digit. Here, the number 4 in 0.4 is in the tenths place. Therefore, -31.4 is named minus thirty-one and four tenths.
  • If the number was -31.45, we would focus on the hundredths place, naming it minus thirty-one and forty-five hundredths.
  • For -31.456, we would look at the thousandths place, naming it minus thirty-one and four hundred fifty-six thousandths.
Understanding both the integer and fractional parts is key to properly naming and interpreting decimal numbers.

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