Understanding the Table of Equivalents

Oct 13, 2025 by thesweetdesigns.com 105 views

Understanding the Table of Equivalents

In mathematics, it is essential to understand the relationships between fractions, decimals, and percentages. This knowledge is crucial in various fields, including finance, science, and engineering. A table of equivalents can help us visualize these relationships and make conversions between different forms of numbers. In this article, we will complete a table of equivalents, rounding decimals to the nearest ten-thousandth and percentages to the nearest hundredth of a percent.

The Table of Equivalents

Fraction	Decimal	Percent
$\frac{1}{2}$	0.50	50.00%
$\frac{1}{4}$	0.25	25.00%
$\frac{3}{4}$	0.75	75.00%
$\frac{1}{8}$	0.125	12.50%
$\frac{3}{8}$	0.375	37.50%
$\frac{5}{8}$	0.625	62.50%
$\frac{7}{8}$	0.875	87.50%
$\frac{1}{16}$	0.0625	6.25%
$\frac{3}{16}$	0.1875	18.75%
$\frac{5}{16}$	0.3125	31.25%
$\frac{7}{16}$	0.4375	43.75%
$\frac{9}{16}$	0.5625	56.25%
$\frac{11}{16}$	0.6875	68.75%
$\frac{13}{16}$	0.8125	81.25%
$\frac{15}{16}$	0.9375	93.75%

Completing the Table of Equivalents

To complete the table of equivalents, we need to find the decimal and percentage equivalents of the given fractions. We can use the following formulas to make these conversions:

Decimal equivalent: Divide the numerator by the denominator.
Percentage equivalent: Multiply the decimal equivalent by 100.

Let's use these formulas to complete the table of equivalents.

$\frac{2}{5}$

Decimal equivalent: $\frac{2}{5} = 0.4$
Percentage equivalent: $0.4 \times 100 = 40.00\%$

$\frac{3}{5}$

Decimal equivalent: $\frac{3}{5} = 0.6$
Percentage equivalent: $0.6 \times 100 = 60.00\%$

$\frac{4}{5}$

Decimal equivalent: $\frac{4}{5} = 0.8$
Percentage equivalent: $0.8 \times 100 = 80.00\%$

$\frac{1}{3}$

Decimal equivalent: $\frac{1}{3} = 0.3333...$
Percentage equivalent: $0.3333... \times 100 = 33.33\%$

$\frac{2}{3}$

Decimal equivalent: $\frac{2}{3} = 0.6666...$
Percentage equivalent: $0.6666... \times 100 = 66.66\%$

$\frac{1}{6}$

Decimal equivalent: $\frac{1}{6} = 0.1666...$
Percentage equivalent: $0.1666... \times 100 = 16.66\%$

$\frac{5}{6}$

Decimal equivalent: $\frac{5}{6} = 0.8333...$
Percentage equivalent: $0.8333... \times 100 = 83.33\%$

$\frac{1}{9}$

Decimal equivalent: $\frac{1}{9} = 0.1111...$
Percentage equivalent: $0.1111... \times 100 = 11.11\%$

$\frac{2}{9}$

Decimal equivalent: $\frac{2}{9} = 0.2222...$
Percentage equivalent: $0.2222... \times 100 = 22.22\%$

$\frac{4}{9}$

Decimal equivalent: $\frac{4}{9} = 0.4444...$
Percentage equivalent: $0.4444... \times 100 = 44.44\%$

$\frac{7}{9}$

Decimal equivalent: $\frac{7}{9} = 0.7777...$
Percentage equivalent: $0.7777... \times 100 = 77.77\%$

$\frac{1}{10}$

Decimal equivalent: $\frac{1}{10} = 0.1$
Percentage equivalent: $0.1 \times 100 = 10.00\%$

$\frac{3}{10}$

Decimal equivalent: $\frac{3}{10} = 0.3$
Percentage equivalent: $0.3 \times 100 = 30.00\%$

$\frac{7}{10}$

Decimal equivalent: $\frac{7}{10} = 0.7$
Percentage equivalent: $0.7 \times 100 = 70.00\%$

$\frac{9}{10}$

Decimal equivalent: $\frac{9}{10} = 0.9$
Percentage equivalent: $0.9 \times 100 = 90.00\%$

Conclusion

$In this article, we completed a table of equivalents, rounding decimals to the nearest ten-thousandth and percentages to the nearest hundredth of a percent. We used the formulas for decimal and percentage equivalents to make the conversions. The table of equivalents is a useful tool for understanding the relationships between fractions, decimals, and percentages. It can be used in various fields, including finance, science, and engineering.<br/> **Frequently Asked Questions (FAQs) about Equivalents of Fractions, Decimals, and Percentages**$

Q: What is the difference between a fraction, decimal, and percentage?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A decimal is a way of expressing a number as a sum of powers of 10. A percentage is a way of expressing a number as a fraction of 100.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert the fraction $\frac{1}{2}$ to a decimal, divide 1 by 2, which equals 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, express the decimal as a sum of powers of 10. For example, to convert the decimal 0.5 to a fraction, express it as $\frac{5}{10}$ , which simplifies to $\frac{1}{2}$ .

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, divide the percentage by 100. For example, to convert the percentage 25% to a decimal, divide 25 by 100, which equals 0.25.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, multiply the decimal by 100. For example, to convert the decimal 0.25 to a percentage, multiply 0.25 by 100, which equals 25%.

Q: What is the table of equivalents?

A: The table of equivalents is a table that shows the relationships between fractions, decimals, and percentages. It is a useful tool for converting between different forms of numbers.

Q: How do I use the table of equivalents?

A: To use the table of equivalents, find the fraction you want to convert in the table, and then look at the corresponding decimal and percentage values. For example, if you want to convert the fraction $\frac{1}{2}$ to a decimal and percentage, look at the table and find the row for $\frac{1}{2}$ , which shows the decimal equivalent as 0.5 and the percentage equivalent as 50%.

Q: What are some common equivalents of fractions, decimals, and percentages?

A: Some common equivalents of fractions, decimals, and percentages include:

$\frac{1}{2}$ = 0.5 = 50%
$\frac{1}{4}$ = 0.25 = 25%
$\frac{3}{4}$ = 0.75 = 75%
$\frac{1}{3}$ = 0.3333... = 33.33%
$\frac{2}{3}$ = 0.6666... = 66.66%
$\frac{1}{6}$ = 0.1666... = 16.66%
$\frac{5}{6}$ = 0.8333... = 83.33%

Q: How do I round decimals to the nearest ten-thousandth?

A: To round decimals to the nearest ten-thousandth, look at the digit in the ten-thousandth place. If it is 5 or greater, round up. If it is less than 5, round down.

Q: How do I round percentages to the nearest hundredth of a percent?

A: To round percentages to the nearest hundredth of a percent, look at the digit in the hundredth place. If it is 5 or greater, round up. If it is less than 5, round down.

Conclusion

In this article, we answered some frequently asked questions about equivalents of fractions, decimals, and percentages. We covered topics such as converting between fractions, decimals, and percentages, using the table of equivalents, and rounding decimals and percentages. We hope this article has been helpful in understanding the relationships between fractions, decimals, and percentages.