English Units Compared to Metric Units
Value in Metric System English System Quantity Unit With Three or More With One or Two Digits Digits 1 in 2.54 cm (exactly) 2.5 cm (4 in) (10 cm) 1 ft 30.48 cm (exactly) 30 cm Length 1 yd 0.914 m1 m 1 mi 1.609 km 1.6 km (100 mi) (160 km) Area 1 ft2 0.0929 m2 0.1 m2 1qt 0.946 L1 L Volume 1 ft3 28.3 L28 L 1 lb. 0.454 kg 0.5 kg Mass (2 lb.) (1 kg) 1 dm2 = 1 dm × 1 dm = 10 cm × 10 cm = 100 cm2
2.54 cm 2.54 cm 4 in × 4 in = 4 in × × 4 in × ≈ 103 cm2 1 in 1 in
SIGNIFICANT DIGITS IN MEASURED AND EXACT QUANTITIES
1. Indicate whether each of the following is a measured (M) or an exact (E) quantity.
5 books ______12 roses ______
5 lb ______16 ounces in one pound ______
9.25 g ______361 miles ______
0.035 kg ______1000 m in 1 km ______
2. State the number of significant figures in each of the following quantities.
6.5 g ______300.0 L ______
0.018 g ______3.9800×1010 atoms ______
0.00608 g ______$2,546, 000 ______
1.360 mL ______655 million beans ______
4.5 m ______204.25 g ______
0.0004 L ______6.25×105 mm ______
805 lb ______34.80 km ______
2.50×10 – 3 L ______8×105 g ______
1200 km ______250. mL ______
1500 meter freestyle swimming ______SCIENTIFIC NOTATION
1. Perform the following mathematical operations without using a calculator.
102 × 105 = ______10–24 × 105 = ______1016 × 10–5 × 10–11 = ______
102 10−3 105 10−4 = ______= ______= ______= ______104 10−6 10−10 1018
2. Write the following numbers in scientific notation.
93 million ______760000000 (3 sig. figs.) ______
0.0001206 ______0.00000450 ______
0.00130 ______0.055×1010 ______
4,450,000 (4 sig. figs.) ______0.00032 ______
38,000 ______25.2 ______
0.0000000021 ______0.0505 ______
3. Write the following numbers in scientific notation.
0.0102×10–3 ______1.9912×10–5 ______
4551×104 ______0.08178×10–3 ______
6022×1020 ______27.21×10–4 ______
4. Write the following as standard decimal numbers.
4.09×102 ______3.00×10–4 ______
5.315×101 ______8.2×10–3 ______
3.150×103 ______2.46×10–6 ______METRIC PREFIXES
1. Fill the blanks in the table.
Prefix milli- kilo-
Symbol n μ d
10n 10‒12 10‒2
2. Perform the following unit conversions by moving the decimal point.
123 cm = m 134000 m = km 50 mg = g
0.0000000206 g = μg 12 mL = L 3600 J = kJ
3. Perform the following unit conversions by moving the decimal point and/or by changing the power of 10. Write the final result either in decimal or in scientific notation which ever seems to be most appropriate in terms of presentation of the final result.
2.98×105 g = μg 7.82×108 g = kg 265 nm = m
536 μL = mL 4.365×1010 cm = nm
1.33×103 nm = pm 8.209×106 km = dm
4. Fill the blanks.
1 yd = ft 1 m = cm
1 yd2 = ft2 1 m2 = cm2
(1yd × 1yd square) (1m × 1m square)
1 yd3 = ft3 1 m3 = cm3
(1yd × 1yd ×1yd cube) (1m × 1m × 1m cube)
5. Perform the following unit conversions by moving the decimal point and/or by changing the power of 10. Write the final result either in decimal or in scientific notation which ever seems to be the most appropriate in terms of presentation of the final result.
569 cm3 = dm3 0.078 pm2 = mm2
7.09×1015 cm3 = μm3 3.67×1019 mm3 = nm3
135600 dm2 = km2 1.35×109 cm3 = mL
6. Complete the table by performing unit conversions. Use scientific notation for numbers that have more than three leading or tailing placeholder zeros.
mm cm dm km
3.20×105 cm
6.9×10−8 km
0.405
7. Complete the table by performing unit conversions. Use scientific notation for numbers that have more than three leading or tailing placeholder zeros.
m3 dm3 L cm3 mL
3.20×105 dm3
6.9×10−8 cm3
0.00601 L
lliM.!2..Read im...English and Metric Ruler uncertain certain (doubtful) •The following are aleo valid "digits" "digit" Illustration llf.m English .aruill..metric measurement fractional notation measurements. /'-... I Example English 11 11 *4" + 314" + 0.5116" 4 + 6/8 + 0.5/16" measurement { I 11 Some rulers will be 4 + 12116 11 + 0.5/16" 1" calibrated to '32 . 11 11 4 + 12.15/16
English---+->-
Centimeters II
, Example metric{ 5 cm+ 0.5 cm+ 0.08 cm = 5.58 cm measurement 50 mm + 5 mm + 0.8 mm = 55.8mm '----- / I certain uncertain digits (doubtful) digit Conversion ll.( Fractional English Measurements tQ. Decimal Engljsh Yiilues
------... ,------... I Fractional I 411 + 314" + 0.5116"
Decimal 4" + 0.75" + 0.03125"
I Decimal 4" + 0.75" I + 0.03" = 4.78" "-----i------I "--·i----I
Certain 11 digits" give Uncertain (doubtful) "digits" give a limited number an unlimited number of significant figures. The doubtful digit here limits of significant figures. the decimal answer to the hundreths place.
English Units Exercise
Decimal Significant Place of Measurement Fractional Notation Value Figures Doubtful Digit Example 4" + 3/4" + 0.5/16" 4.78" 3 0.0X A. B. C. D. E. F.
Metric Units Exercise
Value Significant Figures Place of Doubtful Digit Measurement cm mm cm mm cm mm Example 5.58 55.8 3 3 0.0X 0.X G. H. I. J. K. L.
Calculation Exercise English Units Metric Units Number Place of Number Place of Calculation Answer of Sig. Doubtful Calculation Answer of Sig. Doubtful Figs Digit Figs Digit F − E L − K F × E I × J D + E + F G / H C − A K3 C / A (K – J) / H D / F I / J
- -~------
ineasur-eme.nt-4 How to Read Graduated Cylinders
All meniscuses should be read at the middle - in the case of graduated cylinders the bottom of the meniscus.
\ 50 mL Graduated Cylinder
~------1 ------0 50 ~ ~------! 5 45
10 40 ~ ~ ------1 15 35
20 30 ~ } ____28.3 mL - Example measurement --- 0.3 mL estimated and read ku;t 25 25 ------+3 m.L read serond · ------+25 mL read first 28.3 mL ~ ---- 30 20 ------1 35 15
40 10
45 5 ~------i
I I All meniscuses should be read at the middle - in the case of graduated cylinders the bottom of the meniscus. < +-t---- Two types of 10 mL Graduated Cylinders
e 10 1=~ ·------i... ______,
' 4---=-- fi J 3 === 7 ~ 6.32 mL ._... Example measurement 5= 5 ·------!.______. === ~ ----(0.6) of0.2 mL = 0.12 mL estimated and read [cut 4 --· ;:5:::::::.,. ______----- _ +0.2 mL read seeond _..±l!.. ____ !!!L.. read first 6.32 mL 6===.::::= 4 5 === 5 -- -- 6 -- 4 ~ 1=;; 3~ ------i.______J -- 7 -- 3 o==== z --- -- 8 -- 2 f..o=..t -- 9 -- 1 ~ ·------4.______, ·------i I ~ .. _------I ,,,~ I ~ RULER EXERCISE
Length cm/in Object cm in (decimal name in (decimal (decimal notation) (fractional notation) notation) notation)
Line 1
Line 2
Line 3
Line 4
Line 5
Average Experimental Value for cm/in Ratio:
Accepted Value for cm/in Ratio: 2.54 cm/in
│Exp. Value – Accepted Value│ Percent Error = ×100% = Accepted Value
Line 1 ______
Line 2 ______
Line 3 ______
Line 4 ______
Line 5 ______