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Convert each decimal number to a percent. a. \(0.85\) b. \(1.50\) c. \(0.065\) d. \(1.07\)

Short Answer

Expert verified
a. 85% b. 150% c. 6.5% d. 107%

Step by step solution

01

Understanding the Relationship between Decimals and Percents

To convert a decimal to a percent, we need to understand that a percent is a number out of 100. This means that converting a decimal to a percent involves multiplying the decimal by 100.
02

Conversion of Decimal to Percent for a. 0.85

Multiply the decimal 0.85 by 100 to convert it to a percent: \[0.85 \times 100 = 85\%\]
03

Conversion of Decimal to Percent for b. 1.50

Multiply the decimal 1.50 by 100 to convert it to a percent: \[1.50 \times 100 = 150\%\]
04

Conversion of Decimal to Percent for c. 0.065

Multiply the decimal 0.065 by 100 to convert it to a percent: \[0.065 \times 100 = 6.5\%\]
05

Conversion of Decimal to Percent for d. 1.07

Multiply the decimal 1.07 by 100 to convert it to a percent: \[1.07 \times 100 = 107\%\]

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Key Concepts

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

percentages
In mathematics, a percentage is a way to express a number as a fraction of 100. This makes it a very handy tool for comparing proportions. The word itself, "percent," literally means "per one hundred," indicating that it is a number out of a hundred parts. For example, 85% is a common expression meaning 85 parts out of 100.
Percentages are used in many aspects of daily life such as calculating taxes, interest rates, and discounts. They serve to make it easier to understand the scale of different values since they're always on a standardized base of 100.
To convert a decimal into a percentage, you multiply the decimal by 100. This effectively shifts the decimal point two places to the right, making it straightforward to understand and apply. If you start with a decimal like 0.85, it represents 85 parts out of 100 when multiplied by 100, thus resulting in 85%.
mathematics education
Mathematics education serves as a foundation for teaching students numeracy, logic, and problem-solving skills. Understanding concepts like percentages is essential because they form the basis for more complex ideas that students will encounter later. When teaching these concepts, it's crucial to focus on the why as well as the how.
Here are some strategies to enhance understanding in mathematics education:
  • Practical Examples: Use real-life situations to show where decimals and percentages are applicable. This could be through shopping scenarios where discounts are offered in percentages or savings in a bank account where interest rates are expressed in percentages.
  • Interactive Learning: Tools like online quizzes, interactive apps, or hands-on activities can engage students and make learning about percentages more memorable and enjoyable.
  • Step-by-Step Instructions: As demonstrated in the exercise, showing processes in stages can help students grasp conversions and the logic behind each step.
These strategies not only deepen a student's understanding but also make learning math a more enjoyable experience.
number conversion
Number conversion is an essential part of mathematics that involves changing a number from one form to another, such as from decimals to percentages or vice versa. This skill is not just mathematical but also practical, as it is widely used in everyday life.
The core idea of number conversion from decimal to percent is very straightforward: multiply the decimal by 100. Let's break down this process:
- Multiply by 100: Begin by taking your decimal number and multiply it by 100. - Shift the Decimal Point: This multiplication essentially moves the decimal point two places to the right. - Add the Percent Sign: Finally, add the '%' symbol to denote that it is now a percentage.
Consider an example, the decimal 1.50. By multiplying by 100, the decimal point shifts two places to the right, changing it into 150%. This easy operation converts decimals into a more relatable percentage form for comparison or analysis. Understanding number conversion is crucial for performing everyday calculations quickly and accurately, particularly when budgeting or comparing values.

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Most popular questions from this chapter

A line passes through the points \((-2,-1)\) and \((5,13)\). a. Find the slope of this line. (a) b. Write an equation in point-slope form using the slope you found in 3 a and the point \((-2,-1)\). (a) c. Write an equation in point-slope form using the slope you found in 3 a and the point \((5,13)\). d. Verify that the equations in \(3 \mathrm{~b}\) and c represent the same line. Enter the equations into \(\mathrm{Y}_{1}\) and \(\mathrm{Y}_{2}\) on your calculator, and compare their graphs and tables.

Explain how to find the equation of a line when you know a. The slope and the \(y\)-intercept. b. Two points on that line.

Use the distributive property to rewrite each expression without parentheses. a. \(3(x-2)\) b. \(-4(x-5)\) c. \(-2(x+8)\)

The equation \(3 x+2 y=6\) is in standard form a. Find \(x\) when \(y\) is zero. Write your answer in the form \((x, y)\). What is the significance of this point? (a) b. Find \(y\) when \(x\) is zero. Write your answer in the form \((x, y)\). What is the significance of this point? (a) c. On graph paper, plot the points you found in \(10 \mathrm{a}\) and \(\mathrm{b}\) and draw the line through these points. (a) d. Find the slope of the line you drew in \(10 \mathrm{c}\) and write a linear equation in intercept form. e. On your calculator, graph the equation you wrote in \(10 \mathrm{~d}\). Compare this graph to the one you drew on paper. Is the intercept equation equivalent to the standard-form equation? Explain why or why not. f. Symbolically show that the equation \(3 x+2 y=6\) is equivalent to your equation from \(10 \mathrm{~d}\).

An equation of a line is \(y=25-2(x+5)\). a. Name the point used to write the point-slope equation. (Ti) b. Find \(x\) when \(y\) is 15 .

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