Convert each given fraction and decimal to a percent. 1.) \frac{3}{4} 2.) 0.0043 3.) 1\frac{5}{9} 4.) 5.\overline{2121
The Correct Answer and Explanation is:
To convert fractions and decimals to percents, you multiply the number by 100 and add the percent symbol (%). Let’s convert each one step by step:
1.) 34\frac{3}{4}43
Multiply by 100:34×100=75%\frac{3}{4} \times 100 = 75\%43×100=75%
2.) 0.0043
Multiply by 100:0.0043×100=0.43%0.0043 \times 100 = 0.43\%0.0043×100=0.43%
3.) 1591\frac{5}{9}195
First, convert the mixed number to an improper fraction:159=1491\frac{5}{9} = \frac{14}{9}195=914
Now multiply by 100:149×100=14009≈155.56%\frac{14}{9} \times 100 = \frac{1400}{9} \approx 155.56\%914×100=91400≈155.56%
4.) 5.2121‾5.\overline{2121}5.2121
This repeating decimal means 5.212121…
To convert it to a fraction, let x=5.212121…x = 5.212121…x=5.212121….
Then:100x=521.212121… x=5.212121… Subtract: 100x−x=521.212121…−5.212121…=516⇒99x=516⇒x=51699100x = 521.212121…\ x = 5.212121…\ \text{Subtract: } 100x – x = 521.212121… – 5.212121… = 516 \Rightarrow 99x = 516 \Rightarrow x = \frac{516}{99}100x=521.212121… x=5.212121… Subtract: 100x−x=521.212121…−5.212121…=516⇒99x=516⇒x=99516
Now convert to a percent:51699×100=5160099≈521.21%\frac{516}{99} \times 100 = \frac{51600}{99} \approx 521.21\%99516×100=9951600≈521.21%
Final Answers:
- 34=75%\frac{3}{4} = 75\%43=75%
- 0.0043=0.43%0.0043 = 0.43\%0.0043=0.43%
- 159≈155.56%1\frac{5}{9} \approx 155.56\%195≈155.56%
- 5.2121‾≈521.21%5.\overline{2121} \approx 521.21\%5.2121≈521.21%
Explanation:
To convert any number to a percent, we multiply it by 100 and write the result with a percent symbol. This works because “percent” means “per hundred.” So, turning a number into a percent means expressing it as a part of 100.
For example, with the fraction 34\frac{3}{4}43, we multiply it by 100 to find out how many parts out of 100 that is. 34×100=75\frac{3}{4} \times 100 = 7543×100=75, so 34=75%\frac{3}{4} = 75\%43=75%.
Decimals are even simpler. Just shift the decimal point two places to the right and add a percent symbol. For 0.0043, this gives 0.43%.
When dealing with mixed numbers, like 1591\frac{5}{9}195, we first convert them into improper fractions. This allows us to multiply them directly by 100. Doing so with 149\frac{14}{9}914 gives a percent a little above 100, showing that the number is more than a whole.
Repeating decimals such as 5.2121‾5.\overline{2121}5.2121 take a few extra steps. First, we convert the repeating decimal into a fraction using algebra. Once we find the fraction 51699\frac{516}{99}99516, we multiply by 100 to find the percent. The result shows us that the repeating decimal is equivalent to about 521.21%.
This method can be used for any number, whether it is a whole number, a fraction, or a decimal. The key is always to multiply by 100 and add the percent sign.
