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Chapter 5: Problem 47

Convert the given decimal to a mixed fraction. Do not simplify your answer. 560.453

Short Answer

Expert verified
560 \( \frac{453}{1000} \)

Step by step solution

01

Identify Whole Number and Decimal Part

Start by separating the whole number from the decimal. For 560.453, the whole number is 560 and the decimal part is 0.453.
02

Convert Decimal to Fraction

Take the decimal part 0.453 and convert it to a fraction. Since there are three decimal places, place it over 1000 to become \( \frac{453}{1000} \).
03

Form the Mixed Fraction

Combine the whole number with the fraction obtained. The mixed fraction is 560 \( \frac{453}{1000} \).

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Key Concepts

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

mixed fractions
A mixed fraction, often called a mixed number, combines a whole number with a fractional part. This form allows us to express numbers that are not whole, in a more practical and understandable way.
For instance, when we see a number like 560.453, we can separate it into two parts:
  • The 'whole number', which is 560 in this case.
  • The 'fractional part', which is the decimal that comes after the whole number鈥�0.453.
Using our understanding of mixed fractions, we write this as a combination of a whole number and a fraction. This is how 560.453 becomes 560 \( \frac{453}{1000} \). This mixed fraction represents the exact same value as the decimal, but uses a more traditional numerical format.
decimal numbers
Decimal numbers represent fractions in a linear and straightforward way. They are a crucial aspect of our daily number system, known as the base-10 system. These numbers are composed of whole numbers and a fractional part that follows the decimal point.
For example, the number 560.453 represents:
  • 560, which is the whole number part.
  • 0.453, the fractional part.
The digits after the decimal point each have decreasing fractional values:
  • The first digit after the decimal represents tenths.
  • The second digit represents hundredths.
  • The third digit represents thousandths, and so on.
Understanding each position helps in converting the decimal part into a fraction easily.
fraction conversion
Fraction conversion involves changing a number from one form to another, such as from a decimal to a fraction. This process helps to provide clarity in mathematical operations. To convert a decimal to a fraction:
  • Identify the place value of the last digit in the decimal. For 0.453, this is the thousandths place.
  • Convert the decimal to a fraction by taking the numerator as the digits of the decimal without the point (453 in this case) and the denominator as \(10^n\), where \(n\) is the number of decimal places (1000 here).
So, 0.453 becomes \( \frac{453}{1000} \). Fraction conversion is complete without simplifying, as instructed in some problems. Mastering this conversion is essential for dealing with both exact numbers and scale-based calculations.

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Most popular questions from this chapter

Complete the following tasks to estimate the given square root. a) Determine the two integers that the square root lies between. b) Draw a number line, and locate the approximate location of the square root between the two integers found in part (a). c) Without using a calculator, estimate the square root to the nearest tenth. \(\sqrt{88}\)

Compute the exact square root. If the square root is undefined, write "undefined". \(\sqrt{576}\)

Compute the exact square root. If the square root is undefined, write "undefined". \(-\sqrt{289}\)

Complete the following tasks to estimate the given square root. a) Determine the two integers that the square root lies between. b) Draw a number line, and locate the approximate location of the square root between the two integers found in part (a). c) Without using a calculator, estimate the square root to the nearest tenth. \(\sqrt{12}\)

Greta and Fritz are planting a 13-meter by 18-meter rectangular garden, and are laying it out using string. They would like to know the length of a diagonal to make sure that right angles are formed. Find the length of a diagonal. Round your answer to the nearest hundredth. Your solution should include a well-labeled sketch.
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