Math

QuestionConvert these numbers to scientific notation: 0.000000796, 32640000000000000, 8900000000000, 0.000047. Then convert to standard form: 5.9×10105.9 \times 10^{10}, 8.983×1078.983 \times 10^{-7}, 7.04×10117.04 \times 10^{-11}, 6.1378×1046.1378 \times 10^{4}.

Studdy Solution

STEP 1

Assumptions1. We are asked to express numbers in scientific notation and standard form. . In scientific notation, a number is expressed as a decimal number between1 and10 multiplied by a power of10.
3. For numbers greater than1, the exponent of10 is positive and equals the number of places the decimal point is moved to the left.
4. For numbers less than1, the exponent of10 is negative and equals the number of places the decimal point is moved to the right.

STEP 2

Express the number0.000000796 in scientific notation.
To do this, we move the decimal point7 places to the right, which gives us7.96. The exponent of10 is -7 because the original number is less than1.
0.000000796=7.96×1070.000000796 =7.96 \times10^{-7}

STEP 3

Express the number32640000000000000 in scientific notation.
To do this, we move the decimal point16 places to the left, which gives us3.264. The exponent of10 is16 because the original number is greater than1.
32640000000000000=3.264×101632640000000000000 =3.264 \times10^{16}

STEP 4

Express the number8900000000000 in scientific notation.
To do this, we move the decimal point12 places to the left, which gives us8.9. The exponent of10 is12 because the original number is greater than1.
8900000000000=8.9×10128900000000000 =8.9 \times10^{12}

STEP 5

Express the number0.000047 in scientific notation.
To do this, we move the decimal point5 places to the right, which gives us4.7. The exponent of10 is -5 because the original number is less than1.
0.000047=4.7×1050.000047 =4.7 \times10^{-5}

STEP 6

Express the number 5.9×10105.9 \times10^{10} in standard form.
To do this, we move the decimal point10 places to the right, which gives us59000000000.
5.9×1010=590000000005.9 \times10^{10} =59000000000

STEP 7

Express the number .983×107.983 \times10^{-7} in standard form.
To do this, we move the decimal point7 places to the left, which gives us0.0000008983.
.983×107=0.0000008983.983 \times10^{-7} =0.0000008983

STEP 8

Express the number 7.04×10117.04 \times10^{-11} in standard form.
To do this, we move the decimal point11 places to the left, which gives us0.0000000000704.
7.04×1011=0.00000000007047.04 \times10^{-11} =0.0000000000704

STEP 9

Express the number 6.1378×46.1378 \times^{4} in standard form.
To do this, we move the decimal point4 places to the right, which gives us61378.
6.1378×4=613786.1378 \times^{4} =61378

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