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 5 3 3.20×10 dm −8 3 6.9×10 cm 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 _______________________________________ .