Powers of 10 are super important for changing decimals into fractions and vice versa. This is especially true in Year 7 Math. When students learn how to work with powers of 10, they can quickly and easily make these conversions. That makes learning math a lot smoother!
Powers of 10 are numbers that show how many times to multiply the number 10 by itself. Here are some examples:
When the exponent goes up, it changes the value place, which is very important for turning decimals into fractions and back again.
To turn a decimal into a fraction, a simple way is to write the decimal as a fraction with a number that is a power of 10 in the bottom. Let’s look at the decimal (0.75). We can write it as:
[ 0.75 = \frac{75}{100} ]
Here, (100) is (10^2), so we have used a power of 10 to make a fraction. The next step is to simplify the fraction by dividing both the top and bottom by (25):
[ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} ]
This simplification shows how using powers of 10 can make the process easier.
We can also use powers of 10 to turn fractions into decimals. For example, to change the fraction (\frac{3}{4}) into a decimal, we divide the top number (the numerator) by the bottom number (the denominator):
[ 3 \div 4 = 0.75 ]
Another way is to adjust the fraction so the bottom number (the denominator) is a power of 10. We can multiply both the top and bottom by (25):
[ \frac{3 \times 25}{4 \times 25} = \frac{75}{100} ]
Then, since (100) is (10^2), we can say it equals (0.75) right away.
Division is a big part of these conversions. When you divide by (10), (100), or (1000), it moves the decimal point to the left:
For example:
[ 5.2 \div 10 = 0.52 ]
Turning Decimals into Fractions:
Turning Fractions into Decimals:
Knowing how to use powers of 10 not only helps with changing decimals and fractions but also builds a good base for learning about percentages, ratios, and other math topics later on. Getting a handle on powers of 10 helps students do calculations accurately and become more confident in math!
Powers of 10 are super important for changing decimals into fractions and vice versa. This is especially true in Year 7 Math. When students learn how to work with powers of 10, they can quickly and easily make these conversions. That makes learning math a lot smoother!
Powers of 10 are numbers that show how many times to multiply the number 10 by itself. Here are some examples:
When the exponent goes up, it changes the value place, which is very important for turning decimals into fractions and back again.
To turn a decimal into a fraction, a simple way is to write the decimal as a fraction with a number that is a power of 10 in the bottom. Let’s look at the decimal (0.75). We can write it as:
[ 0.75 = \frac{75}{100} ]
Here, (100) is (10^2), so we have used a power of 10 to make a fraction. The next step is to simplify the fraction by dividing both the top and bottom by (25):
[ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} ]
This simplification shows how using powers of 10 can make the process easier.
We can also use powers of 10 to turn fractions into decimals. For example, to change the fraction (\frac{3}{4}) into a decimal, we divide the top number (the numerator) by the bottom number (the denominator):
[ 3 \div 4 = 0.75 ]
Another way is to adjust the fraction so the bottom number (the denominator) is a power of 10. We can multiply both the top and bottom by (25):
[ \frac{3 \times 25}{4 \times 25} = \frac{75}{100} ]
Then, since (100) is (10^2), we can say it equals (0.75) right away.
Division is a big part of these conversions. When you divide by (10), (100), or (1000), it moves the decimal point to the left:
For example:
[ 5.2 \div 10 = 0.52 ]
Turning Decimals into Fractions:
Turning Fractions into Decimals:
Knowing how to use powers of 10 not only helps with changing decimals and fractions but also builds a good base for learning about percentages, ratios, and other math topics later on. Getting a handle on powers of 10 helps students do calculations accurately and become more confident in math!