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Chapter 8: Problem 22

Write each percent as a decimal number. $$70 \frac{3}{4} \%$$

Short Answer

Expert verified
Question: Convert the percentage 70 3/4% into a decimal number. Answer: 1.45

Step by step solution

01

Convert the whole number part into a decimal

To do this, simply divide the whole number (70) by 100, because there are 100 percentage parts in a whole. $$\frac{70}{100} = 0.70$$
02

Convert the fractional part into a decimal

To convert the fraction (3/4) into a decimal number, divide the numerator (3) by the denominator (4). $$\frac{3}{4} = 0.75$$
03

Add both decimal numbers together

Add the decimal number from the whole number part (0.70) and the decimal number from the fractional part (0.75) together. $$0.70 + 0.75 = 1.45$$ So, $$70\frac{3}{4}\%$$ can be written as a decimal number as: $$1.45$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Fractions to Decimals
Understanding how to convert fractions to decimals is a fundamental math skill. To achieve this, you need to divide the numerator (the top number) of the fraction by the denominator (the bottom number). For instance, if you have the fraction \( \frac{3}{4} \), you would divide 3 by 4. Doing the math gives you:
  • \( \frac{3}{4} = 0.75 \)
This process is pretty straightforward but remembering this step ensures you can convert any fraction into a decimal easily. Practice with different fractions to build confidence. It鈥檚 a key skill that will help you in various math concepts like ratios, percentages, and more.
Performing Decimal Addition
Adding decimals is similar to adding whole numbers, but it鈥檚 important to line up the decimal points to get the correct sum. When adding decimals, every digit must be in the correct place value column, whether it's the tenths, hundredths, or thousandths.
  • For example, if you're adding \(0.70\) and \(0.75\), write them one under the other, ensuring the decimal points are aligned:
  • \[ \begin{array}{c} 0.70 \ + 0.75 \end{array} \]
  • Add as if you're dealing with whole numbers, keeping the decimal point in the same place in your sum:
  • \[ \begin{array}{c} 1.45 \end{array} \]
Make sure you have the decimal points lined up to avoid any mistakes. This practice helps maintain accuracy in calculations, especially when dealing with larger numbers.
Understanding Percent to Decimal Conversion
Percentages are just another way of expressing fractions or decimals. Converting a percentage to a decimal involves dividing by 100, because "percent" means "per hundred". Let鈥檚 take the percentage \(70\%\):
  • Divide by 100: \( \frac{70}{100} = 0.70 \)
  • This means that \(70\%\) is equivalent to 0.70 in decimal form.
When you have a percentage with a fractional part, like \(70 \frac{3}{4}\%\), you convert both the whole number and the fraction to decimals separately and then sum them. It's simple:
  • Whole part: \(70\% = 0.70\)
  • Fractional part: \(\frac{3}{4} = 0.75\)
  • Add them: \(0.70 + 0.75 = 1.45\)
Mastering this technique allows you to handle more complex conversions, making it a handy tool in your math toolkit.

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Most popular questions from this chapter

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