QuestionConvert these numbers to scientific notation or standard form: 3,456,320; 4.563 × 10^{-4}; 0.0004322; 102.0; 7.8322 × 10^{0}; 20,100; 3.40 × 10^{1}; 2.41 × 10^{5}. Fix improper scientific notation: 53.21 × 10^{6}; 125.6800 × 10^{2}; 1003.879 × 10^{-8}; 002368.2 × 10^{-3}.

Studdy Solution

STEP 1

Assumptions1. The numbers are given in decimal notation or in improper scientific notation. . We need to convert the numbers to scientific notation or standard form.
3. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers.
4. In scientific notation, all numbers are written in the form of $a \times10^n$ , where the exponent n is an integer, and the coefficient a is any real number, typically in the range of1 ≤ |a| <10.

STEP 2

First, let's convert the number34. $,456,320$ to scientific notation. To do this, we move the decimal point to the right of the first non-zero digit. The number of places we move the decimal point will be our exponent, n. $,456,320 =.456320 \times10^6$

STEP 3

Next, convert the number35. $.563 \times10^{-}$ to standard form. To do this, we move the decimal point places to the right (because the exponent is -).
$.563 \times10^{-} =0.0004563$

STEP 4

Convert the number36.0.0004322 to scientific notation. To do this, we move the decimal point to the right of the first non-zero digit. The number of places we move the decimal point will be our exponent, n, but it will be negative because we are moving the decimal point to the right.
$0.0004322 =4.322 \times10^{-4}$

STEP 5

Convert the number38.102.0 to scientific notation. $102.0 =1.02 \times10^{2}$

STEP 6

Convert the number39. $.8322 \times10^{0}$ to standard form. Since the exponent is0, the number remains the same.
$.8322 \times10^{0} =.8322$

STEP 7

Convert the number40.20,100 to scientific notation.
$20,100 =2.01 \times10^{4}$

STEP 8

Convert the number37. $3.40 \times10^{1}$ to standard form.
$3.40 \times10^{1} =34.0$

STEP 9

Convert the number41. $2.41 \times^{5}$ to standard form.
$2.41 \times^{5} =241,000$

STEP 10

Now, let's correct the improper scientific notations. For number42. $53.21 \times10^{6}$ , we move the decimal point one place to the left to make the coefficient less than10. The exponent increases by.
$53.21 \times10^{6} =5.321 \times10^{7}$

STEP 11

For number44. $125.6800 \times10^{}$ , we move the decimal point two places to the left. The exponent increases by.
$125.6800 \times10^{} =.256800 \times10^{4}$

STEP 12

For number43. $100.879 \times10^{-8}$ , we move the decimal point three places to the left. The exponent increases by.
$100.879 \times10^{-8} =.003879 \times10^{-5}$

STEP 13

For number45. $002368.2 \times10^{-3}$ , we move the decimal point four places to the left. The exponent increases by.
$002368.2 \times10^{-3} =2.3682 \times10^{}$

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QuestionConvert these numbers to scientific notation or standard form: 3,456,320; 4.563 × 10^{-4}; 0.0004322; 102.0; 7.8322 × 10^{0}; 20,100; 3.40 × 10^{1}; 2.41 × 10^{5}. Fix improper scientific notation: 53.21 × 10^{6}; 125.6800 × 10^{2}; 1003.879 × 10^{-8}; 002368.2 × 10^{-3}.

Studdy Solution

STEP 1

STEP 2

First, let's convert the number34. $,456,320$ to scientific notation. To do this, we move the decimal point to the right of the first non-zero digit. The number of places we move the decimal point will be our exponent, n. $,456,320 =.456320 \times10^6$

STEP 3

Next, convert the number35. $.563 \times10^{-}$ to standard form. To do this, we move the decimal point places to the right (because the exponent is -).
$.563 \times10^{-} =0.0004563$

STEP 4

STEP 5

Convert the number38.102.0 to scientific notation. $102.0 =1.02 \times10^{2}$

STEP 6

Convert the number39. $.8322 \times10^{0}$ to standard form. Since the exponent is0, the number remains the same.
$.8322 \times10^{0} =.8322$

STEP 7

Convert the number40.20,100 to scientific notation.
$20,100 =2.01 \times10^{4}$

STEP 8

Convert the number37. $3.40 \times10^{1}$ to standard form.
$3.40 \times10^{1} =34.0$

STEP 9

Convert the number41. $2.41 \times^{5}$ to standard form.
$2.41 \times^{5} =241,000$

STEP 10

Now, let's correct the improper scientific notations. For number42. $53.21 \times10^{6}$ , we move the decimal point one place to the left to make the coefficient less than10. The exponent increases by.
$53.21 \times10^{6} =5.321 \times10^{7}$

STEP 11

For number44. $125.6800 \times10^{}$ , we move the decimal point two places to the left. The exponent increases by.
$125.6800 \times10^{} =.256800 \times10^{4}$

STEP 12

For number43. $100.879 \times10^{-8}$ , we move the decimal point three places to the left. The exponent increases by.
$100.879 \times10^{-8} =.003879 \times10^{-5}$

STEP 13

For number45. $002368.2 \times10^{-3}$ , we move the decimal point four places to the left. The exponent increases by.
$002368.2 \times10^{-3} =2.3682 \times10^{}$

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QuestionConvert these numbers to scientific notation or standard form: 3,456,320; 4.563 × 10^{-4}; 0.0004322; 102.0; 7.8322 × 10^{0}; 20,100; 3.40 × 10^{1}; 2.41 × 10^{5}. Fix improper scientific notation: 53.21 × 10^{6}; 125.6800 × 10^{2}; 1003.879 × 10^{-8}; 002368.2 × 10^{-3}.

Studdy Solution

STEP 1

STEP 2

STEP 3

Next, convert the number35. .563×10−.563 \times10^{-}.563×10− to standard form. To do this, we move the decimal point places to the right (because the exponent is -)..563×10−=0.0004563.563 \times10^{-} =0.0004563.563×10−=0.0004563

STEP 4

STEP 5

Convert the number38.102.0 to scientific notation.102.0=1.02×102102.0 =1.02 \times10^{2}102.0=1.02×102

STEP 6

Convert the number39. .8322×100.8322 \times10^{0}.8322×100 to standard form. Since the exponent is0, the number remains the same..8322×100=.8322.8322 \times10^{0} =.8322.8322×100=.8322

STEP 7

Convert the number40.20,100 to scientific notation.20,100=2.01×10420,100 =2.01 \times10^{4}20,100=2.01×104

STEP 8

Convert the number37. 3.40×1013.40 \times10^{1}3.40×101 to standard form.3.40×101=34.03.40 \times10^{1} =34.03.40×101=34.0

STEP 9

Convert the number41. 2.41×52.41 \times^{5}2.41×5 to standard form.2.41×5=241,0002.41 \times^{5} =241,0002.41×5=241,000

STEP 10

Now, let's correct the improper scientific notations. For number42. 53.21×10653.21 \times10^{6}53.21×106, we move the decimal point one place to the left to make the coefficient less than10. The exponent increases by.53.21×106=5.321×10753.21 \times10^{6} =5.321 \times10^{7}53.21×106=5.321×107

STEP 11

For number44. 125.6800×10125.6800 \times10^{}125.6800×10, we move the decimal point two places to the left. The exponent increases by.125.6800×10=.256800×104125.6800 \times10^{} =.256800 \times10^{4}125.6800×10=.256800×104

STEP 12

For number43. 100.879×10−8100.879 \times10^{-8}100.879×10−8, we move the decimal point three places to the left. The exponent increases by.100.879×10−8=.003879×10−5100.879 \times10^{-8} =.003879 \times10^{-5}100.879×10−8=.003879×10−5

STEP 13

For number45. 002368.2×10−3002368.2 \times10^{-3}002368.2×10−3, we move the decimal point four places to the left. The exponent increases by.002368.2×10−3=2.3682×10002368.2 \times10^{-3} =2.3682 \times10^{}002368.2×10−3=2.3682×10

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Next, convert the number35. $.563 \times10^{-}$ to standard form. To do this, we move the decimal point places to the right (because the exponent is -).
$.563 \times10^{-} =0.0004563$

Convert the number38.102.0 to scientific notation. $102.0 =1.02 \times10^{2}$

Convert the number39. $.8322 \times10^{0}$ to standard form. Since the exponent is0, the number remains the same.
$.8322 \times10^{0} =.8322$

Convert the number40.20,100 to scientific notation.
$20,100 =2.01 \times10^{4}$

Convert the number37. $3.40 \times10^{1}$ to standard form.
$3.40 \times10^{1} =34.0$

Convert the number41. $2.41 \times^{5}$ to standard form.
$2.41 \times^{5} =241,000$

Now, let's correct the improper scientific notations. For number42. $53.21 \times10^{6}$ , we move the decimal point one place to the left to make the coefficient less than10. The exponent increases by.
$53.21 \times10^{6} =5.321 \times10^{7}$

For number44. $125.6800 \times10^{}$ , we move the decimal point two places to the left. The exponent increases by.
$125.6800 \times10^{} =.256800 \times10^{4}$

For number43. $100.879 \times10^{-8}$ , we move the decimal point three places to the left. The exponent increases by.
$100.879 \times10^{-8} =.003879 \times10^{-5}$

For number45. $002368.2 \times10^{-3}$ , we move the decimal point four places to the left. The exponent increases by.
$002368.2 \times10^{-3} =2.3682 \times10^{}$