(a) Write 0.7 as a percentage.
(b) Write 43.2% as a decimal.
The Correct Answer and Explanation is :
Sure! Here are the answers to your questions:
(a) Writing 0.7 as a Percentage
To convert a decimal to a percentage, you multiply the decimal by 100 and then add the percentage symbol (%).
For 0.7:
[
0.7 \times 100 = 70
]
Thus, 0.7 as a percentage is 70%.
(b) Writing 43.2% as a Decimal
To convert a percentage to a decimal, you divide the percentage by 100.
For 43.2%:
[
\frac{43.2}{100} = 0.432
]
So, 43.2% as a decimal is 0.432.
Explanation
Understanding how to convert between decimals and percentages is crucial in various fields, including finance, statistics, and everyday calculations. A percentage represents a fraction of 100. When you see a percentage like 70%, it means 70 out of 100 parts. Therefore, to find the equivalent in decimal form, you multiply by 100, which effectively shifts the decimal point two places to the right.
In contrast, a decimal is a way of expressing numbers that are not whole. The value of a decimal is determined by its position relative to the decimal point. To express a percentage as a decimal, you need to move the decimal point two places to the left, which corresponds to dividing by 100.
For example, consider a real-world application, such as calculating discounts. If a product costs $100 and is on sale for 30%, to determine the sale price, you convert 30% to its decimal form (0.30) and multiply it by the original price:
[
100 \times 0.30 = 30
]
This indicates a $30 discount, leading to a final price of $70.
These conversions are foundational skills in math, enhancing comprehension in various domains. They facilitate comparisons, calculations, and better decision-making in both personal finance and professional settings.