Multiplying Dividing and by Powers of 10 e I have a special power. Its supernaturally good looks, but I guess I didnt have to tell you that! Mikes Math Mall d a y M s a E Powers of 10 Before we learn how to multiply and divide by Powers of 10, we need to review place value. Rickis Rocko Taconow theres
where I place some value! Place Value The value of a digit depending on its place or position in a number. Lets just focus on numbers for Can you name all of the place values in the number below? 10 tenths hundredths thousandths ten thousandths and hundreds tens ones hundred thousands ten thousands thousands millions
Powers of 8, 374, 625 . 0.1 0.01 0.001 0.0001 Powers of 10 10,00 0 10 1,000 10 0 10 10 10
1 10 10 thousandths hundredths 10 10 tenths 10 ones 10 tens hundreds
10 thousands ten thousands 10 10 10 ten thousandths 10 Notice! As we move to the left on the place value chart, we multiply by 10 to get to each next place. And as we move to the right, we divide by 10 to get to each next 10 place. 10
Powers of 10 In math, a Power of 10 is any integer Example: power of the number ten. In other words, ten multiplied by itself a certain number of times. power or exponent base number Pronounced ten to the third power 10 = 1,000 Powers of 10 Here are a few powers of 10:
Can anyone see a pattern? If you said that each exponent equals the number of zeros in each product, youre right! Powers of 10 This pattern creates a shortcut when we multiply any whole number by a power of ten! Check out the following multiplication problem: 279 100,000 Instead of actually multiplying, we can simply count the number of zeros in 100,000 (which equals ), and add that many zeros tolikes 279. Sparky that shortcut! 1 2
279 100,000 3 4 5 = 1 2 3 4 5 Powers of 10 Lets try some! Multiply the following using the power of 10 rule. 1) 415 1,000 = 3) 233 23,30 100 0 5) 10,000
72 = 2) 1,000,000 56,000,0 56 00 4) 421 10 4,21 = 0 6) 889 720,00 0 88,900,0 100,000 415,00 0 Powers of 10 The Power of 10 principle creates more shortcuts when we multiply or divide decimals! Youre going to show us more shortcuts to make this math junk easier?
Yes, I am! I smell a conspiracy! Just check this out! Powers of 10 Multiplying Decimals Shortcut: Whenever you multiply a decimal by a power of 10, simply move the decimal point to the right the same number of places as there are zeros in the power of 10. In other words: -If you multiply by 10, move the decimal 1 place to the right. -If you multiply by 100, move the decimal 2 places to the right. -If you multiply by 1,000 move the decimal 3 places to the right. And so on
Powers of 10 Lets try some! Multiply the following decimals by simply moving each decimal point. 2) 1) 0.813 81. 100,000 100 = 3 125,5 3) 1.25529 29 91.17 4) 0.85 1,00085 = 911,70 0 10,000 0 6) 1,000,000 5) 10 546.8215,468. = 21 7,900,00
Powers of 10 Dividing Decimals Shortcut: Whenever you divide a decimal by a power of 10, simply move the decimal point to the left the same number of places as there are zeros in the power of 10. In other words: -If you divide by 10, move the decimal 1 place to the left. -If you divide by 100, move the decimal 2 places to the left. -If you divide by 1,000 move the decimal 3 places to the left. Its as simple as Powers of 10 Lets try some more! Divide the following decimals by simply moving each decimal point.
1) 38.95 100 =0.389 5 3) 93.7 10 = 9.3 7 5) 682 1,000 = 0.68 2) 4,01.14 10,0000.0401 = 14 4) 5.1 1,000,000 = 0.00000 51 6) 2,393.7 100,0000.0239 = Powers of 10 Am I dorky if I think this stuff is kinda cool?
Absolutely not! Theres a good chance you were dorky long before this lesson! Thank goodnessWait! What did you just say? Umm.nothing! Just try and remember the following Powers of 10 To multiply a whole number by a power of 10, just add zeros. 0 0 0 0 0
0 0 0 0 0 To multiply a decimal by a power of 10, just move the decimal point to the right. . To divide a decimal by a power of 10, simply move the decimal point to the left. If you can count, YOU CAN DO . Powers of 10 Lastly, lets see how this works with money. Multiply or divide the following money amounts. Round to the 1) $433.68
2) $0.5719 nearest penny. 100 =$4.3 4 3) $1.25 10 = $0.1 3 5) $2.35 = $235.0 1,000 =$571.9 0 4) $9.2487 = $92,487. 00 6) $176,829.19 = $1.7 Mikes Math Mall