called supernaturally by Ten Multiplying Dividing Made Easy of and Powers I have a special power. It’s called supernaturally good looks. CCSS 5.NBT.A.1 & 5.NBT.A.2 Mike’s Math Mall

Ricki’s Rocko Taco…now there’s where I place some value! Powers of 10 Before we learn how to multiply and divide by Powers of 10, we need to review place value. Ricki’s Rocko Taco…now there’s where I place some value! Place Value – The value of a digit depending on its place or position in a number. Let’s just focus on numbers for awhile, Sparky!

Can you name all of the place values in the number below? Powers of 10 Can you name all of the place values in the number below? hundred thousands ten thousandths ten thousands thousandths thousands hundredths millions hundreds tenths ones tens and 8, 374, 625 . 7914 0.1 0.01 0.001 0.0001

Powers of 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 place. ÷ 10 ÷ 10 ÷ 10 ÷ 10 ten thousandths ten thousands thousandths thousands hundredths ÷ 10 ÷ 10 hundreds ÷ 10 ÷ 10 . tenths ones tens × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 𝟏 𝟏𝟎 𝟏 𝟏𝟎𝟎 𝟏 𝟏,𝟎𝟎𝟎 𝟏 𝟏𝟎,𝟎𝟎𝟎 10,000 1,000 100 10 1

Powers of 10 In math, a Power of 10 is any integer power of the number ten. power or exponent Example: 10 3 base number In other words, ten multiplied by itself a certain number of times. Pronounced “ten to the third power” 10 3 =10 × 10 × 10 = 1,000

Powers of 10 Can anyone see a pattern? Here are a few powers of 10: 𝟏𝟎 𝟏 =𝟏𝟎 𝟏𝟎 𝟐 =𝟏𝟎×𝟏𝟎=𝟏𝟎𝟎 𝟏𝟎 𝟑 =𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏,𝟎𝟎𝟎 𝟏𝟎 𝟒 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏𝟎,𝟎𝟎𝟎 𝟏𝟎 𝟓 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏𝟎𝟎,𝟎𝟎𝟎 𝟏𝟎 𝟔 =𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎=𝟏,𝟎𝟎𝟎,𝟎𝟎𝟎 Can anyone see a pattern? If you said that each exponent equals the number of zeros in each product, you’re right!

Powers of 10 This pattern creates a shortcut when we multiply any whole number by a power of ten! Instead of actually multiplying, we can simply count the number of zeros in 100,000 (which equals 𝟏𝟎 𝟓 ), and add that many zeros to 279. Check out the following multiplication problem: 1 2 3 4 5 1 2 3 4 5 279 × 100,000 = 27,9 00,000 Sparky loves that shortcut!

Powers of 10 Let’s try some! 1) 415 × 1,000 = 415,000 2) 1,000,000 Multiply the following using the Powers of 10 rule. Let’s try some! 1) 415 × 1,000 = 415,000 2) 1,000,000 × 56 56,000,000 3) 233 × 100 4) 421 × 10 = 4,210 23,300 6) 889 × 100,000 5) 10,000 × 77 = 770,000 88,900,000

to show us more shortcuts to make this math junk easier? Powers of 10 The Power of 10 principle creates more shortcuts when we multiply or divide decimals! You’re going to show us more shortcuts to make this math junk easier? I smell a conspiracy! Just check this out! Yes, I am!

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 Let’s try some! 1) 0.813 × 100 = 81.3 2) 100,000 Multiply the following decimals by simply moving each decimal point. Let’s try some! 1) 0.813 × 100 = 81.3 2) 100,000 × 1.25529 125,529 3) 91.17 × 10,000 4) 0.85 × 1,000 = 850 911,700 6) 1,000,000 × 7.9 5) 10 × 546.821 = 5,468.21 7,900,000

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. It’s as simple as counting!

Powers of 10 Let’s try some more! 1) 38.95 ÷ 100 = Divide the following decimals by simply moving each decimal point. 1) 38.95 ÷ 100 = 2) 401.14 ÷ 10,000 = 0.3895 0.040114 3) 93.7 ÷ 10 = 4) 5.1 ÷ 1,000,000 = 9.37 0.0000051 5) 682 ÷ 1,000 = 6) 2,393.7 ÷ 100,000 = 0.682 0.023937

Powers of 10 Absolutely not! Thank goodness…Wait! What did you just say? Am I dorky for thinking this stuff is kinda cool? Absolutely not! There’s a good chance you were dorky long before this lesson! Umm….nothing! Just try and remember the following information…

If you can count, YOU CAN DO THIS! Powers of 10 To multiply a whole number by a power of 10, just count and 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 THIS!

Powers of 10 Lastly, let’s see how this works with money. Multiply or divide the following money amounts. Round to the nearest penny. 1) $433.68 ÷ 100 = 2) $0.5719 × 1,000 = $4.34 $571.90 3) $1.25 ÷ 10 = 4) $9.2487 × 𝟏𝟎 𝟒 = $0.13 $92,487.00 5) $2.35 × 𝟏𝟎 𝟐 = 6) $176,829.19 ÷ 𝟏𝟎 𝟓 = $235.00 $1.77

Powers of 10 You certainly don’t need help in that area, Sporticus! I’m afraid I can’t help you there! You certainly don’t need help in that area, Sporticus! Now that I have this Powers of 10 thing down, do you think you could do me another favor? Do you have any special powers on getting rid of little sisters, or making burritos magically appear? Then how about one for attracting the ladies? I guess you’re right! Hey! Who wants to see a belly wave? Wow! My job here is done! I guess I can try! What is it, Sparkington? © Mike’s Math Mall