7/16 into Decimal: A Comprehensive Guide to Converting Fractions

Converting fractions into decimals is a fundamental mathematical skill that finds applications in various fields, including science, engineering, finance, and everyday life. One common fraction that we often encounter is 7/16, which represents a value less than 1. In this article, we will delve into the different methods of converting 7/16 into decimal, providing step-by-step instructions, examples, and helpful tips.

Long Division Method

The long division method is a straightforward approach to converting fractions into decimals. It involves dividing the numerator (the top number) by the denominator (the bottom number) using long division.

Step 1: Set up the division: Write the numerator as the dividend and the denominator as the divisor, using long division format. Example:

16 ) 7

Step 2: Perform the division: Divide the first digit of the dividend by the divisor to get the first digit of the decimal. In this case, 7 divided by 16 is 0.

Step 3: Bring down the next digit: Bring down the next digit of the dividend next to the remainder. In our case, the next digit is 0.

Step 4: Perform the division again: Divide the new number by the divisor to get the next digit of the decimal. 70 divided by 16 is 4.

Step 5: Repeat steps 3-4: Continue bringing down digits and performing the division until you reach the desired level of accuracy.

Using the long division method, we can convert 7/16 into decimal as follows:

16 ) 7.0000
     64
     ----
      60
      48
      ----
      120
      128
      ----
       -80

Therefore, 7/16 = 0.4375.

Decimal Fraction Method

The decimal fraction method involves converting the fraction into an equivalent fraction with a denominator of 10, 100, 1000, and so on. We then remove the denominator to obtain the decimal representation.

Step 1: Find an equivalent fraction: Multiply both the numerator and denominator of the given fraction by the same number to create an equivalent fraction with a denominator of 10, 100, or 1000. In this case, we multiply by 25:

7/16 = (7 x 25)/(16 x 25) = 175/400

Step 2: Remove the denominator: Remove the denominator of the equivalent fraction to obtain the decimal representation. In this case, we remove 400, which gives us:

175/400 = 0.4375

Therefore, 7/16 = 0.4375 using the decimal fraction method.

Proportion Method

The proportion method involves setting up a proportion between the given fraction and its decimal equivalent. We then cross-multiply and solve for the unknown decimal value.

Step 1: Set up the proportion: Set up a proportion by equating the given fraction to the decimal representation:

7/16 = x

Step 2: Cross-multiply: Cross-multiply the numerators and denominators:

7 x 1 = 16 x x

Step 3: Solve for x: Solve the equation for x by dividing both sides by 16:

x = (7 x 1) / 16 = 0.4375

Therefore, 7/16 = 0.4375 using the proportion method.

Examples

1. A store is selling apples for $0.75 per pound. If you buy 3/4 of a pound of apples, how much will it cost?

Solution: To find the cost, we need to multiply the price per pound by the weight of apples:

Cost = $0.75 x 3/4 = $0.75 x 0.75 = $0.5625

Therefore, it will cost $0.5625 to buy 3/4 of a pound of apples.

2. A recipe for chocolate chip cookies calls for 2/3 cup of chocolate chips. If you are making a double batch of cookies, how many cups of chocolate chips will you need?

Solution: To find the number of cups of chocolate chips needed, we need to multiply the amount of chocolate chips in the original recipe by 2:

Chocolate chips needed = 2/3 cup x 2 = 4/3 cup = 1 1/3 cups

Therefore, you will need 1 1/3 cups of chocolate chips to make a double batch of cookies.

3. A survey found that 5/8 of respondents prefer coffee over tea. If 1200 people were surveyed, how many people prefer coffee?

Solution: To find the number of people who prefer coffee, we need to multiply the fraction of people who prefer coffee by the total number of respondents:

Number of people who prefer coffee = 5/8 x 1200 = 750

Therefore, 750 people prefer coffee out of the 1200 people surveyed.

What We Learn from These Examples

• Converting fractions into decimals is essential for solving real-world problems involving measurements, money, and percentages.
• The long division method, decimal fraction method, and proportion method are all reliable techniques for converting fractions into decimals.
• Understanding the concept of equivalent fractions allows us to manipulate fractions to make calculations easier.

Tips and Tricks for Converting Fractions

• If the denominator of the fraction is a power of 10 (e.g., 10, 100, 1000), you can easily convert the fraction to a decimal by moving the decimal point to the left the same number of places as the power of 10. Example: 3/100 = 0.03.
• If the numerator and denominator of the fraction are both odd, you can simplify the fraction by dividing both numbers by their greatest common factor (GCF). This will make the division process easier. Example: 9/15 = (3 x 3)/(3 x 5) = 3/5.
• When using the long division method, it's helpful to write the decimal point directly above the dividend, which ensures that the decimal point in the answer is in the correct place.
• If you get a repeating decimal when using long division, you can express the decimal as a fraction using the following formula:

Decimal = Numerator / (Denominator - Remainder)

How to Convert 7/16 into Decimal Step-by-Step

1. Choose a conversion method: You can use any of the three conversion methods discussed earlier: long division, decimal fraction, or proportion.
2. Perform the conversion: Follow the steps outlined for your chosen method.
3. Round the answer: If necessary, round the answer to the desired level of accuracy.

Call to Action

Converting fractions into decimals is a fundamental mathematical skill that is widely used in various fields. By understanding the different conversion methods and practicing regularly, you can improve your mathematical abilities and confidently handle problems involving fractions and decimals.