The chip book-to-bill ratio may still be under water, but it is now floating so close to the surface that it can clearly be seen, and shares of semiconductor fabricators rallied yesterday on hopes that the worst really is over. At 0.99, the book-to- bill ratio, reported by the US Semiconductor Industry Association late Tuesday, is at its highest this year, and compares with a revised 0.93 in August. The rise reflected a stronger-than-expected increase in new orders, which climbed 9% on the August figure at $3.19bn. Shipments for September rose 2.1% to $3.22bn compared with the August figure. The improvement is put down to better demand from personal computer makers and more stable prices for memory chips. Texas Instruments jumped $1.125 t o $56.25 and National Semiconductor added 50 cents to $20.375; Applied Materials Inc, which makes fabrication equipment, rose $1 to $29 on Nasdaq. Micron Technology Inc said last week that its excessive inventories of memory chips had fallen to desirable levels, and its shares were up 25 cents at $32.375. Since mid-September, memory prices have risen 30% to 50% from their lows. Worldwide, the ratio rose to 0.97 in August from 0.95 in July. Global figures include Asia, Europe, North America and Japan and are one month behind North American figures. The book-to-bill ratio for the Japanese market rose above 1.0. North American orders for the month were still 32.1% below September 1995 order level of $4.7bn, when the ratio was standing at 1.16. Shipments were 20% below the $4.06bn figure of a year earlier.