Metric Prefix worksheet

1. In quettaA: 3.25e-30 QA

1. Each prefix is a power of ten: milli is 10^-3 and quetta is 10^30

   $\text{1 mA = 10^-3 A; 1 QA = 10^30 A}$

2. Subtract the exponents to get the shift: -3 − (30) = -33, so move the decimal point 33 places left

   $\mathrm{3,250}\text{\hspace{0.17em}mA}\times {10}^{\mathrm{-33}}$$=3.25e-30\text{\hspace{0.17em}QA}$

2. In hectobit: 2.2e-11 hbit

1. Each prefix is a power of ten: pico is 10^-12 and hecto is 10^2

   $\text{1 pbit = 10^-12 bit; 1 hbit = 10^2 bit}$

2. Subtract the exponents to get the shift: -12 − (2) = -14, so move the decimal point 14 places left

   $\mathrm{2,200}\text{\hspace{0.17em}pbit}\times {10}^{\mathrm{-14}}$$=0.000000000022\text{\hspace{0.17em}hbit}$

3. In zettaV: 2.2e-6 ZV

1. Each prefix is a power of ten: tera is 10^12 and zetta is 10^21

   $\text{1 TV = 10^12 V; 1 ZV = 10^21 V}$

2. Subtract the exponents to get the shift: 12 − (21) = -9, so move the decimal point 9 places left

   $\mathrm{2,200}\text{\hspace{0.17em}TV}\times {10}^{\mathrm{-9}}$$=0.0000022\text{\hspace{0.17em}ZV}$

4. In ronnaJ: 2.7e-6 RJ

1. Each prefix is a power of ten: exa is 10^18 and ronna is 10^27

   $\text{1 EJ = 10^18 J; 1 RJ = 10^27 J}$

2. Subtract the exponents to get the shift: 18 − (27) = -9, so move the decimal point 9 places left

   $\mathrm{2,700}\text{\hspace{0.17em}EJ}\times {10}^{\mathrm{-9}}$$=0.0000027\text{\hspace{0.17em}RJ}$

5. In deciPa: 0.03 dPa

1. Each prefix is a power of ten: micro is 10^-6 and deci is 10^-1

   $\text{1 µPa = 10^-6 Pa; 1 dPa = 10^-1 Pa}$

2. Subtract the exponents to get the shift: -6 − (-1) = -5, so move the decimal point 5 places left

   $\mathrm{2,500}\text{\hspace{0.17em}µPa}\times {10}^{\mathrm{-5}}$$=0.025\text{\hspace{0.17em}dPa}$

6. In petaPa: 2e-42 PPa

1. Each prefix is a power of ten: quecto is 10^-30 and peta is 10^15

   $\text{1 qPa = 10^-30 Pa; 1 PPa = 10^15 Pa}$

2. Subtract the exponents to get the shift: -30 − (15) = -45, so move the decimal point 45 places left

   $\mathrm{2,000}\text{\hspace{0.17em}qPa}\times {10}^{\mathrm{-45}}$$=2e-42\text{\hspace{0.17em}PPa}$

7. In picoΩ: 1.6e+36 pΩ

1. Each prefix is a power of ten: zetta is 10^21 and pico is 10^-12

   $\text{1 ZΩ = 10^21 Ω; 1 pΩ = 10^-12 Ω}$

2. Subtract the exponents to get the shift: 21 − (-12) = 33, so move the decimal point 33 places right

   $\mathrm{1,600}\text{\hspace{0.17em}ZΩ}\times {10}^{33}$$=1.6e+36\text{\hspace{0.17em}pΩ}$

8. In petabit: 2.5e-33 Pbit

1. Each prefix is a power of ten: zepto is 10^-21 and peta is 10^15

   $\text{1 zbit = 10^-21 bit; 1 Pbit = 10^15 bit}$

2. Subtract the exponents to get the shift: -21 − (15) = -36, so move the decimal point 36 places left

   $\mathrm{2,500}\text{\hspace{0.17em}zbit}\times {10}^{\mathrm{-36}}$$=2.5e-33\text{\hspace{0.17em}Pbit}$

9. In rontoH: 3,700 rH

1. Each prefix is a power of ten: ronto is 10^-27 and ronto is 10^-27

   $\text{1 rH = 10^-27 H; 1 rH = 10^-27 H}$

2. Subtract the exponents to get the shift: -27 − (-27) = 0, so the value doesn't change

   $\mathrm{3,700}\text{\hspace{0.17em}rH}\times {10}^0$$=\mathrm{3,700}\text{\hspace{0.17em}rH}$

10. In zeptoHz: 3.25e+54 zHz

1. Each prefix is a power of ten: quetta is 10^30 and zepto is 10^-21

   $\text{1 QHz = 10^30 Hz; 1 zHz = 10^-21 Hz}$

2. Subtract the exponents to get the shift: 30 − (-21) = 51, so move the decimal point 51 places right

   $\mathrm{3,250}\text{\hspace{0.17em}QHz}\times {10}^{51}$$=3.25e+54\text{\hspace{0.17em}zHz}$