Decimals: Learn It 2

Write a Decimal as a Fraction

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that [latex]$5.03[/latex] means [latex]5[/latex] dollars and [latex]3[/latex] cents. Since there are [latex]100[/latex] cents in one dollar, [latex]3[/latex] cents means [latex]{\Large\frac{3}{100}}[/latex] of a dollar, so [latex]0.03={\Large\frac{3}{100}}[/latex].

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[/latex], the [latex]3[/latex] is in the hundredths place, so [latex]100[/latex] is the denominator of the fraction equivalent to [latex]0.03[/latex].

[latex]0.03={\Large\frac{3}{100}}[/latex]

For our [latex]$5.03[/latex] lunch, we can write the decimal [latex]5.03[/latex] as a mixed number.

[latex]5.03=5{\Large\frac{3}{100}}[/latex]

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

How To: Convert a Decimal Number to a Fraction or Mixed Number

  1. Look at the number to the left of the decimal.
    • If it is zero, the decimal converts to a proper fraction.
    • If it is not zero, the decimal converts to a mixed number.
      • Write the whole number.
  2. Determine the place value of the final digit.
  3. Write the fraction.
    • numerator—the ‘numbers’ to the right of the decimal point
    • denominator—the place value corresponding to the final digit
  4. Simplify the fraction, if possible.

Rounding Decimals

Rounding decimals is a mathematical procedure used to simplify numbers, making them easier to work with or communicate. It involves looking at the digits in a number and determining whether to increase the digit in the specific place value based on the digit that follows it. The goal is to find the nearest number at the specified place value, whether it be the nearest whole number, tenth, hundredth, etc.

When discussing rounding decimals, it’s crucial to understand the concept of place value. Place value refers to the value of a digit depending on its position within a number. For example, in the number [latex]123.45[/latex], the digit ‘[latex]2[/latex]‘ is in the tens place and is worth [latex]20[/latex], while the digit ‘[latex]4[/latex]‘ is in the tenths place and is worth [latex]0.4[/latex].

How To: Rounding Decimals

  1. Locate the given place value and mark it with an arrow.
  2. Underline the digit to the right of the given place value.
  3. Is this digit greater than or equal to [latex]5?[/latex]
    • Yes – add [latex]1[/latex] to the digit in the given place value.
    • No – do not change the digit in the given place value
  4. Rewrite the number, removing all digits to the right of the given place value.
If the digit to the right of your given place value is [latex]5[/latex] or above, give your given place value a shove.  If the digit to the right of your given place value is [latex]4[/latex] or less, let your given place value rest.