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Chapter 5: Problem 538

In the following exercises, name each decimal. $$ -12.5632 $$

Short Answer

Expert verified
Negative twelve and five thousand six hundred thirty-two ten-thousandths.

Step by step solution

01

Identify the Characteristic (Whole Number Part)

Look at the number to the left of the decimal point. Here it is -12.
02

Identify the Mantissa (Decimal Part)

The number to the right of the decimal point is 5632. This is the mantissa.
03

Write the Fraction

Represent the number 0.5632 as a fraction: \(\frac{5632}{10000}\).
04

Combine Characteristic and Mantissa

Combine the characteristic and the decimal fraction: -12 and 0.5632.
05

Write in Words

Write out the whole number and the fraction in words: negative twelve and five thousand six hundred thirty-two ten-thousandths.

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Key Concepts

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

Characteristics of a Decimal Number
In any decimal number, the characteristic is the whole number part to the left of the decimal point. For instance, in the number -12.5632, the characteristic is -12. This part is crucial for understanding the decimal fully, as it tells us the magnitude and the sign of the number.

Think of the characteristic as the base or the foundation of the decimal number. When you see -12, it immediately tells you that our number is negative and has a value greater than 12 when ignoring the decimal part.

Always look for the characteristic first, as it sets the stage for the entire number.
Understanding the Mantissa
The mantissa is the part of the decimal number that comes after the decimal point. In the number -12.5632, the mantissa is 5632. This portion tells us the finer details of the number and helps to increase its precision.

If you think of the characteristic as the building, then the mantissa is the intricate details inside. It refines the characteristic and provides a more accurate value.

By separating the characteristic and mantissa, we can clearly see how big the number is and just how precise it is. This practice is a fundamental part of understanding decimal numbers.
Fraction Representation of Decimals
To better understand the relation between decimals and fractions, consider representing the mantissa as a fraction. For -12.5632, the decimal part (mantissa) 5632 can be written as \(\frac{5632}{10000}\).

Here's how to do it:
  • Identify the decimal places. 5632 has four decimal places.
  • Write the number as the numerator.
  • Use 1 followed by as many zeros as there are decimal places as the denominator 鈥� in this case, 10000.
  • Simplify the fraction if possible.
Combining the characteristic and the fraction gives us the full picture: -12.5632 is -12 + \(\frac{5632}{10000}\). Writing this in words, it translates to negative twelve and five thousand six hundred thirty-two ten-thousandths.

This practice not only helps in naming decimals but also enhances understanding of their structure.

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