Fractions, decimals and percentages
One number, three disguises: they are all the same point on the number line.
Which decimal is 31%?
Our number system works in tens, so 10, 100 and 1000 fit easily with decimals. A calculator needs a decimal, not a percentage.
Which decimal is the same as 31%?
What this lesson covers
The idea
Since our number system is base 10, a denominator of 100 fits easily with decimals, so a fraction, its decimal and its percentage are interchangeable forms of the same number (x% = x/100).
Which decimal is 31%?
Our number system works in tens, so 10, 100 and 1000 fit easily with decimals. A calculator needs a decimal, not a percentage.
Which decimal is the same as 31%?
- 3.1
- 0.31
- 0.031
Slide along the line
The marker shows one number on the line from 0 to 1. Read it as a fraction, a decimal and a percentage. Find the three numbers in the goal.
Three forms of one number
Since our number system is base 10, a denominator of 100 fits easily with decimals, so a fraction, its decimal and its percentage are interchangeable forms of the same number (x% = x/100).
Two examples: 31% = 31/100 = 0.31 50% = 50/100 = 1/2 = 0.5
Percent to decimal: divide by 100. Decimal to percent: multiply by 100.
Why bother with percentages? Sugar is 9/34 of Variety 1 and 13/45 of Variety 2. Which is more sugary? It is hard to tell. As percentages it is clear: 26.47% and 28.89%, so Variety 2 is more sugary.
Notes
Since our number system is base 10, a denominator of 100 fits easily with decimals, so a fraction, its decimal and its percentage are interchangeable forms of the same number (x% = x/100).
Check yourself
Write 7% as a decimal.
Answer: 0.07
7% = 7/100 = 0.07.
Write 0.45 as a percentage.
Answer: 45 %
0.45 = 45/100 = 45%.
Which of these is not the same number as 3/5?
Which is bigger: 0.4 or 35%?
- 0.35 — correct. Right! 3/5 = 60/100 = 0.6. And 0.35 is 35%.
- 0.6. 3/5 = 60/100 = 0.6, so it is the same number.
- 60%. 3/5 = 60/100, which is 60%, so it is the same number.
- 6/10. 3/5 = 6/10 (multiply the top and the bottom by 2), so it is the same number.
- 0.4, because 0.4 is 40% — correct. Yes! 0.4 = 40/100 = 40%, and 40% is more than 35%.
- 35%, because 35 is more than 0.4. The two are written differently. 35% is 0.35, and 0.4 is more than 0.35.
- They are equal. 0.4 is 40% and 35% is 0.35, so they are different.