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Chapter 4: Problem 49

Which number is larger? $$ 0.004, \frac{4}{100} $$

Short Answer

Expert verified
0.04 is larger than 0.004.

Step by step solution

01

Convert Fraction to Decimal

Convert the fraction \(\frac{4}{100}\) into a decimal. To do this, divide the numerator (4) by the denominator (100). This calculation gives:\[ \frac{4}{100} = 0.04 \]
02

Compare Decimals

Compare the two decimal numbers: 0.004 and 0.04. Notice that 0.04 has a higher value than 0.004.
03

Determine the Larger Number

From the comparison, it is clear that 0.04 is greater than 0.004.

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Key Concepts

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

fraction to decimal conversion
To solve exercises that involve comparing a fraction with a decimal, the first step is to convert the fraction into its decimal form. This process is known as 'fraction to decimal conversion'. Converting a fraction to a decimal involves dividing the numerator (the top part of the fraction) by the denominator (the bottom part of the fraction). For example, to convert the fraction \(\frac{4}{100}\) to a decimal, divide 4 by 100. This gives: \[\frac{4}{100} = 0.04\] Now, you have a decimal that can be easily compared with other decimal numbers.
decimal place value
Understanding 'decimal place value' is crucial for comparing decimal numbers. Each digit in a decimal number has a specific place value depending on its position relative to the decimal point. For example, in the number 0.123, the '1' is in the tenths place, the '2' is in the hundredths place, and the '3' is in the thousandths place. When comparing decimal numbers, you start by comparing the digits in the highest place value (tenths), and then move to the next place value (hundredths), and so on, until a difference is found.
In the provided exercise, the numbers to compare are 0.004 and 0.04.
  • The number 0.004 has its '4' in the thousandths place.
  • The number 0.04 has its '4' in the hundredths place.
    Since hundredths come before thousandths, 0.04 is clearly the larger number.
comparing decimal values
Once you have converted all numbers to their decimal form and understood their place values, you can begin 'comparing decimal values'.
This process involves:
  • Lining up the decimal points of the numbers
  • Comparing digit by digit from left to right until you find a difference
For instance, comparing 0.004 and 0.04:
At the tenths place, both numbers have '0', so move to the next position. At the hundredths place, 0.04 has a '4' while 0.004 has '0'.
Hence, 0.04 is greater than 0.004.
In conclusion, comparing decimal numbers involves intuitive steps that start with conversion, understanding place values, and then a direct comparison to determine which number is larger.

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