Video Transcript
Find the difference between 0.034 and nineteen twenty-fifths. Round your answer to the nearest tenth.
As we’re trying to calculate the difference between a decimal and a fraction, our first act is to convert them into the same type. In this case, we will convert nineteen twenty-fifths, or 19 over 25, into a decimal. One way of doing this is to type 19 divided by 25 into our calculator, as the line in a fraction means divides. If, however, we did not have a calculator, we need to convert the fraction into an equivalent one with a denominator of 100.
25 multiplied by four is equal to 100. Remember, with fractions, whatever we do to the bottom, we must do to the top. Therefore, we must multiply 19 by four. This is equal to 76. 10 multiplied by four is 40. And nine multiplied by four is 36. Adding these gives us 76. We can therefore say that the fraction 19 over 25 is equivalent to 76 over 100.
Instead of dividing by 25, we can now divide by 100. When dividing by 100, all the digits move two places to the right. 76 divided by 100 is equal to 0.76. This means that the fraction 19 over 25 is equivalent to 0.76. We’re asked in the question to find a difference between the two numbers. This means we need to subtract them. The larger decimal is 0.76. So, we need to subtract 0.034 from this.
When performing column subtraction, we can add a zero to even up the columns. As we can’t subtract four from zero, we need to borrow one from the hundredths column. 10 minus four is equal to six. In the hundredths column, five minus three is equal to two. And in the tenths column, seven minus zero equals seven. Zero minus zero is equal to zero. And we keep our decimal point in the same place. 0.76 minus 0.034 is equal to 0.726.
We were asked to round our answer to the nearest tenth. This is the same as rounding to one decimal place. As the number in the hundredths column is a two, we will round down. 0.726 rounded to the nearest tenth is 0.7. We can therefore say that the difference between 0.034 and nineteen twenty-fifths is 0.7 to the nearest tenth.
